Irrespective of in universe reasons (i.e. prime vs. JJ universes), wasn’t there a break up between CBS and Paramount a couple of years ago, which was one of the reasons why Discovery didn’t happen last year in the 50th anniversary. There was a contractual stipulation that CBS couldn’t launch a new series within 6 months of a new movie.
On the other hand, I read the Star Trek Discovery novel Desperate Hours which scratches some of that itch. In it Burnham and Spock team up and have to deal with their shared history, Saru meets Number One and Captain Pike butts heads with Captain Georgiou .
Edit: I watched episode 7…I really enjoyed it. I thought it was the most Trekkie episode they’ve done so far. And Stammets is turning out to be my favourite character.