Most ordinary mods (.esp, .esm, .esl, and loose meshes and textures) should be unaffected-those are not version-dependent.* However, if you are updating your game that is always a good time to revisit the modpages, read the changelogs, and update your mods if MO2 shows available updates. (Read carefully, MO2 will show available updates not necessarily relevant to your specific modlist).

Skse is always version dependent; it performs a version check to avoid memory address errors and will only work with it's intended version number. Most mods that require skse are also version dependent and will need to be updated. A general rule of thumb is any mod with a .dll file needs to be checked for compatibility.

Here is a fairly comprehensive list of many major skse-dependent mods and which game versions they are intended for. You will need to be certain that you install a version of these mods intended for the game version you are running.
https://modding.wiki/en/skyrim/users/skse-plugins

*The Unofficial Patch (USSEP) was updated to account for the new content beginning with game ver. 1.6.1130. Do not use the current version of the patch with older versions of the game. If you backport, however, some new .esl files need this mod to run on 1.5.97 or older. https://www.nexusmods.com/skyrimspecialedition/mods/106441 Unless you personally are good at modding and sorting out your own compatibility issues backporting is usually not a good idea.

The safest practice would be to start a new game after updating your mods.