No, Ober does not need to go 7 innings. That's not what starting pitchers do anymore. Pineda is barely averaging more than 5 innings per start. If Ober can consistently go 5 innings and keep the team in the game he's a 4th starter.
I'm skeptical that we see the Twins bring up many of the real pitching prospects. Strotman, Balazovic and Duran are on the 40 man roster so we could see them but they will not want to add players early. They already need to evaluate Jax, Barnes, Thorpe, Gant, Burrows, Alcala and Garcia to see if they are worth keeping for 2022. Remember that you don't get to add the whole 40 man in September anymore.