Torch flames and trees swaying in the wind do not affect gameplay at all - they're most likely done in a shader and I think it's easier to keep updating a time uniform than to add extra conditions everywhere :D

That's usually because the system that runs those things is independent of the timing of the main game loop. And then when someone finally gets around to implementing the pause screen, they still run even with the main game time stopped. And you look at it and think "eh, you know what - looks cool - we'll leave it".

Against the Storm (and excellent rouguelite city-builder) does this in a really cool way. Pausing is a core mechanic of the game, and you frequently pause while you place building or things like that - and all the visual animations stop (fire, rain, trees swaying, etc).

But when you find a broken ancient seal in the forest, the giant creepy eyeball moving around in it keeps moving even when you pause the game, which helps emphasise how other-worldly it is.

I find it confusing: for me a clear indicator the game is paused is all animations also pausing. Some games do not pause in menu’s, for example. And some do, but not when in a multiplayer session

I think it really just depends on the game and what purposes “pausing” serves in that game. Take a game like solitaire, for example: there is no meaningful “pause” feature you could add, since the game state only advances in response to a user action.

Other pause some underlying simulation while still letting you modify the game state, as an expected part of gameplay, like a city builder. As the user might spend a significant amount of time in a paused state building things, it would be pretty visually unappealing to have the entire world completely frozen the whole time.

Others might pause all gameplay entirely, such as for displaying a menu, in which case pausing even environmental animations might make more sense since the user isn’t actively playing.

For the second type, I would much prefer some GUI element to indicate the simulation is paused rather than freezing the whole game world, such as a border around the screen or maybe a change of color theme of the GUI or similar.

It's nice when a bug manifests as a feature.

I'm the opposite, it drives me crazy! Along with sound effects / music playing.