Well, I played through the tutorial and a couple false-starts, then finished my first Federation play-through (on minimal difficulty). There are obviously some bugs and QOL issues (they could probably just do a group-replace of "FTL" for "warp," some neutral fleets had a "Borg" icon, one early Borg mission never depopulated, there's a literal mission about founding Deep Space Nine, but all the space stations around Bajor are the generic alien design, not the specific Cardassian one). Bajor being integrated into the Cardassian Union caught me by surprise, but I was able to send an envoy over to annoy them into starting a war with me, so I was able to liberate it (and a few other systems). I was disappointed that the Klingons allied with the Cardassians during the war, but for some reason, they just didn't care for me on this run the way they had before.
There was another odd thing, that was probably down to how Stellaris works. I was on pretty good terms with the Romulans the whole time through, and did the evacuation (that should probably a bit more hands-on than just "build one big transport then you're done), but they never really warmed to me. The culmination was after Romulus was destroyed, I surveyed the system, claimed it, then built an orbital habitat and colonized with a ship full of Romulans. I felt that was still a little weird, though, but then I noticed I could cede (some) systems in the trade deal box. I had a maxed out starbase, a very expensive artificial world, already populated by their own people, and the Romulans were so disinclined to trade with me that I had to throw in ten thousand tons of alloys without asking for anything back to get them to agree.
Part of it's probably down to having the game set to easy, but by that point I was maxing out on resources, no one was bothering me I had my science and science-adjacent ships on auto-survey, and was filling in starbases and mines sometimes, but not as a priority. The game had just gotten too big to manage by that point. I had dozens of fleets in the sidebar, hundreds of empty ones in the fleet manager, dozens of planets and starbases, even with them all set to "auto," and once I found the pirate headquarters and made peace, that was pretty much the end of things, and then I was waiting for ages with next to nothing happening, researching new technologies to get the Sovereign-class blueprints so I could reach the end of the mission tree (to be fair, I'd already won on "Civics" a while earlier, but that was very anticlimactic). Raising the cap for an individual fleet helped make that more managable, but it should've happened much earlier in the game, especially considering how having governments join the Federation inflates your fleet count (especially with useless, uncommanded science ships). By the time the Borg actually came, I was able to smash them easily. It probably would've been more challenging if they'd been quicker on the draw with their invasion instead of sitting at the highway nodes and waiting for me to come to them, with only a couple of ships actually attacking.
I do agree that this does feel very "beta." There's areas of polish missing (oddly, the Enterprise-D has custom textures, but the Enterprise-E doesn't), some strange decisions (I would've flipped the Intrepid and the Excelsior in the tech-tree, at the least), and I could use some more diplomacy options, especially among the big four (I couldn't figure out how to even ask the Romulans to help me with the Klingons and the Cardassians. You evacuate an entire homeworld, and that's the thanks you get...).