Some thoughts:
A lot of the episode felt pretty paint-by-numbers generic scifi. We got small ships dog fighting in space, a marketplace with strange aliens and holograms. Security guards with lasers that shoot from their fists. We got a lovable rogue character who is a smuggler. It all felt very Star Wars. The floating holo screens from your arm are also pretty standard scifi stuff. The table that morphs and ondulates with hand gestures to control stuff looks cool and and futuristic, but is pretty generic scifi stuff. It kinda reminded me of Krypton in Man of Steel.
There were definitely some far fetched moments like Michael hitting a space ship and then falling through the atmosphere and surviving. For one, space is so vast that the odds of her exiting a wormhole and hitting a space ship maneuvering at high speed is infinitely small. Also, it is mighty convenient that Michael's red angel suit can protect her from colliding with a ship at high speed in space and survive re-entry into an atmosphere even with her restarting the thrusters at the last second. And Book somehow having the ability to summon magical plants that can heal was also weird.
My favorite part of the episode by far was the final scene with unfurling the flag of the Federation. That really moved me. I love the Starfleet guy who waited for 40 years. Very touching. Beautiful scene.
I imagine that the spore drive will allow the Discovery to visit different Federation worlds and help them rebuild. But I am concerned that the entire season might end on a big reset button. After all, if Discovery figures out what caused the Burn and they return to their own time in the past, they can prevent the Burn from ever happening which would make that future never happen. I would prefer Discovery never return to their own time and this future stay fixed but with a new and better Federation.
I am also left with a lot of questions about "the burn". How did all the dilithium just explode? That seems odd. What about other modes of transportation that don't rely on dilithium? Shouldn't the Federation have been able to continue with space travel with other forms of FTL especially since this takes place some 600+ years after TNG. Surely, Starfleet would have transwarp, quantum slipstream or some other forms of FTL not yet invented that do not use dilithium.
Also, a lot can happen in the 150 years since the Burn. Since the Burn apparently destroyed all or most of Starfleet's ships, the Federation would have been virtually defenseless. So did enemies like the Romulans, Dominion or Borg invade the Federation immediately after the Burn?
Also, how big was the Federation right before the Burn happened? Considering that it was hundreds of years in the future, a lot could happen. Did the Federation expand and colonize the Delta Quadrant or the Gamma Quadrant? Did the Federation become a galactic civilization?
Also, I am intrigued that the Starfleet guy said that he could only scan about 30 sectors. That means there could potentially be remnants of Starfleet and the Federation beyond his scans. Maybe in the 150 years since the Burn, parts of the Federation have rebuilt and the starfleet guy just does not know about it since he is cut off?
I am certainly intrigued to see where the season will go.