At the casino, I carry extra chips in my pocket that are not in play yet. I use those chips to top off my stack whenever it goes below 100 BB. As long as I respect the maximum buy-in rule, can I simply just add chips to my stack? Or do I have to let the dealer know? What's the rule, and what's the etiquette?
Yes you can. It's like going to the cage for chips, getting chips from a runner or anything else like that. Dealer doesn't need to be involved. There are no rules being broken.
No rules are being broken if you respect the maximum buy in rule, but the way that you add chips could be seen as bad etiquette.
An example of good etiquette:
You have a $200 stack consisting of all 5$ chips. You get involved in a hand and end up losing $20. you take $20 in red chips from your pocket and add them to your stack so that everyone at the table can see all the chips in your stack.
An example of bad etiquette/angle shooting:
You have a $200 stack consisting of all 5$ chips. You lose $100 in a hand and now have half the stack. you take a $100 chip out of your pocket and place it on the table where it is hidden from the other players' view.
I assume you are not angle shooting, but it may be helpful to be aware that sometimes the way you add chips to your stack could be seen as shooting an angle by other players.