A menu I open with a keyboard shortcut should just be there. A dialog I open a few times a day can take a moment to show up. These are different problems, and the easing curve isn't what makes them different.
So I start by counting. How many times a day will someone see this move?
Hundreds of times, from the keyboard: no animation. Think of a command menu, a shortcut, or a toggle you hit without looking. Any motion there just sits between pressing the key and getting the result. Raycast opens with no transition at all, and that's the right call for a tool people use all day.
Dozens of times, in passing: barely anything. A row you hover can change color in about 150ms. It shouldn't slide, fade up, or wait for the rows around it. By the tenth time, a staggered animation doesn't feel polished anymore. It just feels slow.
A few times per session: this is where motion actually helps. Dialogs, drawers, toasts. The movement shows where the thing came from, which is also where it'll go when it leaves. A drawer that slides up from the bottom can be swiped back down. A toast that comes in from a corner shows you which way to swipe it away before you even try.
Once, or close to it: a first success, a celebration, an empty state. That's where you can afford something slower, so save it for there.
Take a settings page as an example. People flip the theme toggle all the time, so the icon just swaps and the page doesn't animate. The "delete account" dialog is rare, so it can fade and scale in from 0.95. Not from 0, though. scale(0) makes it look like the dialog appeared out of nowhere. A small scale with a fade makes it look like it was there all along.
If I can't say why something moves, I don't animate it. Good reasons are things like feedback, showing where something came from, smoothing a change so it doesn't pop, or explaining something on a page that's meant to teach. "It looks cool" isn't one of them, at least not in something people use every day.
Pages of writing fail this test right away. People come to read. If the text starts at opacity 0, the first thing they see is a blank page. The text can just be there.