It’s not the same universe and that’s all there is to it.
No, it is the same universe. You don't own Star Trek and don't get to decide whether or not it's all the same universe. Paramount owns Star Trek, and Paramount says it's all the same universe. You can personally reinterpret it as a separate universe in your own mind, but that's not the actual text. The actual text is that it's all the same universe.
Lower Decks to regular Trek is like Hot Shots to Top Gun.
No, Lower Decks is to regular Star Trek as The Mary Tyler Moore Show is to Lou Grant.