MattCMK Upgrading from 3.8 to 4.1 will often not affect your skeletons and animations at all, but rotation animations may be affected due to changes in the rotation specification. In 3.8 and earlier, rotation could not be keyed to values greater than 360 degrees, but with the redesigned Graph view in 4.0, it is now possible to add keys for rotations greater than 360 degrees. This can cause the rotation to reverse between some keys, or behave differently if some animations are mixed at runtime, although this is rare.

For more information on this change, the following thread may be helpful:
https://esotericsoftware.com/forum/d/17550-rotate-not-working--unable-to-type-round-numbers

Could any features from older assets disappear or stop working?

Although some buttons have been moved or disappeared due to changes in the editor's UI, there is no change that would cause the animation itself to stop working. However, it is possible that a fixed bug may cause your skeleton or animation to behave differently than before, so the only way to be sure that the skeleton and animations are working as expected is to actually check them after the upgrade. You may want to test it first with a few projects, and if it seems to be OK, proceed to upgrade.