NATO is not something you can just apply to on a whim. The path for a membership was there: e.g. there were some joint exercises, etc. Obviously they also need political integration as well.

Russia actually have been a member of Council of Europe (PACE, etc.) since 1996 but it was expelled in 2022. If they had a good record in Council of Europe they could really go for NATO membership eventually.

Never ever that was a thing. There has never been any applications to have Russia as NATO member. What Putin was referring and had in mind was not exactly NATO membership but special treatment to Russia, that would allow using benefits of NATO, by not submitting to anything.