This community inspired me to buy and restore my first hand planes

That's a perfectly reasonable question.
Bench planes are used for taking rough lumber and squaring and smoothing it for use. If you only buy wood from the hardware store you're used to seeing "S4S" or "surfaced four sides" boards, so it's already been squared and smoothed by machines. If you buy your wood from a specialty wood dealer, it usually comes rough. In both cases it's usually not really square and straight, so you'll need some means to remove warp, twist, cupping, etc.
Hand planes are the old-school tool for the job. Longer planes flatten longer boards, and shorter planes are used to smooth and clean up after the rough work from the earlier planes. I'm in danger of just recapitulating this article by Chris Schwarz, so I might as well link the whole thing:
https://www.popularwoodworking.com/wp-content/uploads/CoarseMediumFine.pdf
This is an excellent explanation of which planes you need, what they're used for, and how to set them up for that use.

As you already know from your door work, a plane slices shavings of wood whereas sandpaper basically just chews away making dust.

The result is that the plane produces extremely smooth surfaces. Smoother than any sandpaper you're likely to use. Did I mention the dust?

If you have a fair bit of material to remove, but not so much that a saw is useful, a decent plane with a sharp blade on a well supported workpiece will often do the job faster than a sander. Yes you can start with a coarse grit and get ever finer until you have both the right dimensions and a smooth enough surface, but the plane is smooth all the way and the amount removed in one pass is based on how thick a shaving you take. That makes it easier to "sneak up" on your dimensions. A reasonable compromise is to start with coarse sandpaper and finish with a plane, but did I mention the dust?

A plane takes a bit of time to get tuned up, but once done, it rarely requires more than sharpening. Once you get the hang of sharpening, it doesn't take much longer than swapping out sandpaper (except for the those Velcro-like sanding disks), but a plane doesn't produce dust.

As you can tell, I hate dust. Unless you spend a fortune on dust collection, dust will always get everywhere, making a general mess, spoiling finishes, and clogging lungs. I've never heard of a dust collection system that eliminates the need to wear good PPE.

As a bonus, setting up the plane the right way with a sharp blade lets you take nice curls of wood, even from scrap, that can be turned into wood "roses" and such for decorations, gifts, or the craft market. The regular shavings can be bagged up and used (and even sold!) for kindling, small animal cages, or mulch. Be careful with your wood species, though, as some are toxic. All the more reason to avoid creating dust! :) As far as I can tell, wood dust is basically just a potentially harmful substance, even from non-toxic specifies, with few if any practical uses.

About the only place I like to use sandpaper is to do a quick pass by hand with a medium or coarse grit to roughen a surface for gluing or to get a mechanical bond with additional coats of epoxy when I let the previous coat cure too long.

Ha, that's odd, I don't have them marked as NSFW. Imgur has been weird with that stuff since they decided to ban nude content a few months ago.