Please Update AI memory

For example i use android studio and it already has a stable version 35 of compileSdk and targetSdk, but cursor is disagreeing with me about that and uses old ones 34. Also sometimes it uses old version of imports.

Can i handle it somehow myself?

This does not happen on the cursor side, but the knowledge is in the AI ​​model that you are using
If your prompt contains a generalized form for installing something without specifying the version and you are getting unsatisfactory results, then I recommend simply specifying the version during installation (clearly stating in the prompt which version you are interested in) and preferably, if there have been any changes in new versions, specify the basic necessary data from the documentation (what you are using) and then the AI ​​will easily take this into account and do what you need
You can insert this data from the documentation (changes in the new version) into .cursorrules and everything should work fine