True, as far as I know there are only the bull and the bear markets, which are the only seasons available on this environment. They are always ignited by a major movement in Bitcoin's price. If BTC goes up, we enter a bullish season and if Bitcoin goes down we enter a bearish season.

Altcoins don't have any influence on this process. It's quite the opposite, they are heavily influenced by the process.

I think what OP says about altcoin, memecoin, NFT seasons could be replaced by altcoin, memecoin, NFT hypes, what is also a consequence of the seasons, but not the seasons themselves.