I think I understand what you mean. A physical body does obey laws of physics and thus restricts the "true freedom" of a whisp or spirit. However, a hröa can also focus and direct the energies innate to a fëa, which could make the being more powerful. In Fëanor's case, his fëa was the brightest and strongest of all the elves, and when he died, his hröa actually disintegrated due to the power of his fëa leaving, so one could argue (without much evidence) that his spirit was stronger than a physical body could truly handle (but this falls apart when looking at Morgoth or the other Vala's bodies that don't burn up).
There's not a lot of text specifically surrounding the fëa and hröa, but some of it can be gleaned from the silmarillion, or unfinished tales. Tolkien liked his mysticism a lot more in the earlier drafts of the legendarium, so unfinished tales will probably suit you more (although some of those drafts aren't considered "canon" in light of the silmarillion's later publishing and research, but that's another matter entirely).
You're exactly right with Sauron. He was originally able to shape shift into anything (fun fact: his first appearance was Tevildo Lord of cats, then altered to Thû the necromancer who could turn into a werewolf, then finally Sauron), but after the fall of Númenor, he lost that ability and was left with his body looking dark and evil. By pouring his fëa into the one ring, he risked total doom by its destruction since he wouldn't have enough power left to maintain even a spiritual form on middle earth.
I don't think there's any evidence that a Maiar with a hröa is weaker than a Maia without a hröa. There's no interaction between a pure fëa Ainur and an embodied Ainur, so there's no way to get a definitive answer. I would say that without a hröa, the fëa can't be "focused" and is therefore weaker (from the wiki (no source provided): "According to the Elves, the fëa is powerless without the hröa, and likewise the latter would die without the former.")
Huh, you do get what I mean. Have you ever imbibed any illicit substances, or just good narratives? (I'm hoping the answer is "both", but I don't judge.)
However, a hröa can also focus and direct the energies innate to a fëa, which could make the being more powerfu
That's a very good point.
I don’t think there’s any evidence that a Maiar with a hröa is weaker than a Maia without a hröa.
I don't think "weaker". I just think limited until the body burns up and their full might is revealed, sort of. Like if they had to fight another maia, that is. Like a huge bodybuilder in a weird costume that limits their actions, but if you actually started a fight with them, they'd just punch you "for real" and the cardboard of their costume wouldn't be in the way, it'd just tear off while they're punching you through the costume.
I would say that without a hröa, the fëa can’t be “focused” and is therefore weaker (from the wiki (no source provided):
I get your point, but I think it's more about the sort of fight that's going on. Like if you have a lense, it's not gonna make the light source more powerful, but it can focus it into a neater beam, making it more powerful in that spot, but then that focusing would mean that there's less light going around "the room" in general. Like a beam of light that's as powerful as an orb of light would burn your eyes if directed at you, but also, would be less blinding than an orb of light if directed away from you. So in that sense, the hröa being able to focus power would be a positive and a negative, depending on the type of environment/enemy you're facing.
I get what you're saying, but it doesn't work that way in middle earth according to Tolkien. We have lots of instances of Ainur vs Ainur combat where they don't pop out of their hröa for more power. The best example is the war of wrath where the host of the valar (including Eönwë, a Maia) goes against Morgoth, the mightiest of the valar, and there's no mention of that happening. It could be that Tolkien omitted it, but that's a big enough fight that I think it would have been mentioned if it occured
Well, the pure power wouldn't matter if it wasn't concentrated enough to destroy the hröa their enemies was using to influence the Seen, I guess. Like they'd have first destroy their enemies physical being to be able to influence their incorporeal being?
And to do that, you'd want to focus your power, so you'd need a "lens" of sorts, meaning you'd use a body to fight the enemy?
Oh wait no, Morgoth didn't have a physical body in that fight? Uh, I'd probably do well to read the Silmarillion again lol.