When it comes to giving characters an internal dialogue - for most types of narration, it should be limited to the PoV character, of which there usually is one per scene or even chapter or entire story - so your hunch of keeping it limited to the protagonist was correct. The only type of narration where the thoughts of all characters would be revealed to the reader is third person omniscient, end even then, it can easily get confusing to have the thoughts of many people thrown around like nobody's business. In third person limited or first person limited narration, we see the world through the perspective of one of the characters, and thus can't know what other characters are thinking, though we can learn what our PoV character
thinks others are thinking.
There's a difference in using internal dialogue for exposition and for exploring a character. A lot of it comes down to the "show, don't tell" rule I mentioned earlier - a quick Google search will tell you all about it, better than I can anyway, but in short - plainly giving away information feels both unnatural, and less engaging for the reader. When you think about it, we rarely speak or think about things obvious to us. This conclusion is most often wordless, comes afterwards, and is best left up to the reader themselves. For example, the expression "This is a Sunday, the day the office is closed." doesn't tell us much about the character whose thoughts we're reading, and only provides us with the fact that today is a Sunday and most people don't work. (Unless the point is that the character has robotic mannerisms and works off pure logic - but in that case, it'd be nice to underline that for the audience through other means as well). It shows the logical conclusion one's brain would come to, but it'd be more interesting if it showed how that conclusion was formed. For instance, what do you think about this variant (not saying this is how it should be written. It might not fit the character you have in mind):
He raised an eyebrow and double-checked his memory with a calendar hanging in one of the cubicles. It was indeed a Sunday. Who in the right mind would want to work on a Sunday?
It's not much, but we learn a tiny bit about the character here - he's either forgetful or unsure of himself, hence he checks whether his memory is correct before forming an opinion, and he doesn't like the idea of working on a Sunday, which begs the question of why is he himself on call, while also establishing that he's at odds with his interlocutor. All while still telling the reader that it's a Sunday, a day which is unusual for office work.
This example also has a different structure - it starts off with regular narration, and then transitions into the character's mind with the last sentence, without the need for italicised text or a "he thought" tag, making it a bit smoother, though that's just purely personal preference. You can then resume normal narration like nothing happened.
I found this article, which goes in detail about the strengths of internal dialogue, the many forms it can take, with many examples, so you don't have to learn about it from my bias:
https://www.janefriedman.com/internal-dialogue/
Again, some searching about the topic of writing internal dialogue will give you much more to work with. There's even many threads on the FA forums that helped me immensely with this kind of stuff, though they are rather old and you might need to do some digging.