I think him and Elon Musk probably talked about him and using X more. I think they were both at Donald Trump’s inauguration, so it probably happened then.
Nice speculation, but it doesn't seem to be the case.
There has been one full calendar month since the inauguration, February. Cook tweeted or reposted 8 times that month.
January was 15 posts or reposts.
December was 25.
November was 9.
October was 16.
I have a feeling that Cook is posting what he feels he needs to based on Apple's communications strategies, and not because he may or may not have talked to Musk or anyone outside of Apple about it.