Mix of both light and deeper shows here, mostly character-driven:
Scrubs - Show about a group of residents at a hospital navigating their first few years of training.
Cougar Town - Show about 40somethings in western Florida, the name has nothing to do with the show after the first five or ten episodes. Same creator as Scrubs. Focuses on the core group navigating life at 40 in Florida and their ridiculousness.
Community - Show about a community college in Colorado that gets increasingly experimental in its story telling. Show focuses on the antics of the core group.
Better Off Ted - Another show about 40somethings, this time in the corporate world. The name, like Cougar Town, has almost nothing to do with the actual show. Focuses on how this group tries to keep ahead of their soul crushing jobs for a corporation that's literally evil.
Happy Endings - This time about 30somethings in Chicago who are all friends, two of whom are about to get married when the bride runs away at the altar. Really turns into putting this group into various scenarios to see how it plays out.
New Girl - Show about a teacher in LA who moves into a loft with three guys (sometimes a fourth) and their subsequent misadventures in the city.
30 Rock - Show about the cast and crew of an SNL-style variety show airing weekly on NBC out of 30 Rockefeller Plaza in New York, grows increasingly absurdist over times.
Arrested Development - About the son of a real estate tycoon who gets arrested for so many crimes and how he tries to keep the family business going despite the incompetence of the rest of the family (and occasionally his own incompetence).
Bored to Death - About a writer who solves mysteries with his publisher and best friend (two different people).
Only Murders in the Building - Show about three residents, two older and one younger, of a classic New York residential building that discover they like the same murder mystery podcasts and then start their own true crime podcasts when they discover a murder occurred in their building.
Veep - About a put-upon Vice President of the United States and the general incompetence of her office and the administration. Surprisingly insightful satire of the actual executive branch in the United States.
Silicon Valley - Show about a group of guys in Silicon Valley and their VC partners trying to build a startup.
Happy to recommend more if you've got something more specific you're into.
The Good Place (a show about moral philosophy and the afterlife. This may sound dry, but watch the first couple episodes. They're not very long, trust me)
Good Omens (based on a Terry Prachett novel about an angel and a demon who become friends and then have to thwart the coming of the end-times to save humanity and their relationship)
Columbo (it's more detective show than comedy, but it's about a bumbling detective who seems to know whodunnit within 5 minutes of showing up to the crime scene, but then spends +45min whittling away at the murderer's psyche until they either crumble and confess, make a mistake, or he finds the evidence he's been looking for)
Monk (also comedic detective show, this one about a detective suffering from severe OCD after his wife died in a carbomb. I know the premise sounds dark, trust me, the shows' really funny and generally fairly light)
Psych (aaand another comedic detective show, this time about a man who's extremely perceptive and tries to help the police out on a case, but is too good at it and is accused of being the murderer. He then comes up with the claim of being a psychic to avoid getting arrested and then proceeds to get contracted by the cops as a psychic detective)
UK Top Gear/The Grand Tour (comedy car shows)
If you feel like you need something dark and disturbing, but with a bit of humor to it:
Utopia (2013 UK version, NOT THE 2020 AMAZON VERSION)
This series is one of the best shows I've watched, but it's also possibly the darkest, most disturbing TV show I've ever watched. The pandemic only made it worse. I put this here, however, because while it's primarily a conspiracy thriller, there is a fair amount of black comedy in it. I want to recommend watching it, even just for the relatively unique use of framing and cinematography, but jesus christ this show does not shy away from showing you things most directors would leave to the imagination.
Not sure about what constitutes a light comedy, but The Righteous Gemstones is a fantastic show I just got turned onto a few months ago. Good news is it just wrapped up season 3, so there's plenty to watch.
If you want some quirky Britishness you might try Coupling. It was written by Steven Moffat, who you may remember as the head writer for Doctor Who during the Matt Smith era, and if you liked the humor during that run then you'll probably love Coupling.
Detectorists - light hearted, warm and funny show about the lives of metal detector enthusiasts. Got to be my favourite British show to come out in years.
Not new, but new to me.. Vice Principals on HBO Max was so good... So much better than Eastbound and Down. Danny Mcbride and Walton Goggins' chemistry was amazing, and one of the best bromances ever.
It's a bit vulgar, so that may dissuade some people. It's only 2 seasons but it's the best comedy series I've watched for a while.
Green Wing. It's a British sitcom set in a hospital. There's absolutely nothing medical-related in it; the hospital is just the place where everyone works - a backdrop and nothing more. It's somewhere between a sketch show, a soap opera and a comedy drama - it's surreal, exaggerated and definitely has a lot of "sketch-like" scenes, but the characters are fleshed out and consistent, and have proper emotional arcs.
It has an absolutely fantastic cast, and a lot of them have gone onto have very successful careers since then. Olivia Coleman, for one, but I'm sure you'll recognise Tamsin Greig, Stephen Mangan, Michelle Gomez and Mark Heap - if not their names then at least their faces.
It has an incredible editing style and score, too. Like, it's impossible not to notice how good they are, even if they're not something you're usually remotely interested in. In particular, it makes heavy use of slow-motion and fast-forward at the start and end of scenes, with the brilliantly catchy score as the only audio, which really highlights the actors' body language as well as making for great transitions between scenes.
It's laugh-out-loud funny, memorable and surprisingly endearing for such a surreal show. I always found it surprising that Black Books - which is also fantastic (and also stars Tamsin Greig) - managed to find an American audience but Green Wing never seemed to. Both are on par with each other, I think.
"Derry Girls" and "Pen15" are both hilarious and perfectly capture the awkwardness of being a teenage girl. I actually had to ask my husband to leave the room during Pen15, because it felt like he was watching footage of my most embarrassing moments.
Edit to add: if you have HBO, we've also really been enjoying "The Righteous Gemstones". It's about a family that runs a megachurch. "White Lotus", which is about rich people on vacation, isn't really what I would call a lightheaded comedy... but it's definitely funny! Especially the first season.
Definitely not in the same genre but I can’t recommend Taskmaster enough. All the seasons are good but I’d start with a series that has a comedian you know you like in it and binge from there!
If you liked Abbot Elementary, you'll also like Home Economics. Coincidentally I only watched it because it started auto playing after Abbot Elementary finished.
A lot of good suggestions in this thread, but for a combo of what you've already watched (Abbott Elementary and the British version of Ghosts) Bad Education is a comedy about a subpar British teacher.
If you've not watched Mork and Mindy, that's worth it. It was Robin William's breakout role in television, so if you know Robin, you know what you're getting. It's delightful.
I've been really getting into Korean tv on Netflix lately, too. Best watched with subtitles and no dubbing.
My gf and I have been watching Good Manager, which is about a tacky mob accountant trying to run away from his problems by skimming flagrantly from all of the dodgy businesses he manages.
He gets hired at a large corporation and thinks he's onto his biggest scam yet, but the accounting team are sincere, the managers are psychos, and he's still got a glimmer of heart beneath his red hair dye and 1980's Sears catalogue suits that makes stealing from big business really, really hard when they take it out on the little guy.
It's had me absolutely rolling; people's facial expressions, their theatrics, and vigorous use of the leitmotif really brought it together. 10/10, for me.