I wonder how they'd rationalize it. I think if they'd done this, they should have done it like an anthology where each character has the same personality but is canonically a different person, almost as if Boimler, Mariner, Tendi, and Rutherford were character actors.
The maroon uniform era would be complicated; you'd need to figure out how to set it far enough so that they don't exist too close to either the TOS or TNG versions. I'd say the 2320s or 2330s ( roughly when Picard was in the Academy) so that they're all retiring by the start of DS9.
I'm not sure if DSC era proper would work well as a setting for a Trek comedy - I'm not sure there's enough to joke about for a whole season, and I think the overall tone of the 32nd century setting doesn't work well for a comedy. However, either a pre-burn future (mid 25th-30th) or maybe a few decades to a century after Discovery when the Federation's back on its feet might be nice.
I might recommend a 2-in-1 Thinkpad. I can’t speak for all models, but my 1st generation Surface Go brought me misery when running Debian Testing on it - power profiles weren’t supported quite right and the camera was hard to set up.
If you have the budget, the Star Lite seems pretty nice as a Linux tablet, although you should do your own research - I don’t own one. Personally, I have a Thinkpad E16 for college.