So, i've been playing more actively for the last couple of days and here is my list of things that in my opinion need attention of developers. First - more important ones, followed by minor things like bugs.
1. Ship refit is way too expensive. Upgrading just ONE fighter to the next level weapon (from 2 to 3 or 3 to 4) costs 137 gold\credits. I'm on turn ~ 120 and make about 50-60 gold per turn. So, the income of my whole large empire is not enough to upgrade the weapon of one little fighter ? Something is very off here, obviously. In my opinion, refit cost should be at least 5-6 times less, so that upgrading that fighter would cost me about 20-30 gold. For cruisers and battleships the price can substantially higher (like 100-200 gold).
2. Ship refit is very inconvenient. Refit button allows only to select one ship and a design you want to upgrade it to. There must be a way to upgrade multiple ships in a fleet all at once, if they are of the same design.
3. Ok, I actually figured out how to do that. One thing i have to say is that it should be more obvious maybe. [It must be possible to change an existing ship design, instead of deleting an old one and creating new every time new modules are available.]
4. Different treaties with other civs require a certain level of "relations". At first I confused it with their opinion of you, but then figured out they are different things, since numbers don't add up. Now, the only way to know current level of relations (I know of) is to hover over treaty you can't propose (because relation lvl is too low) and it will tell you that, for example, level 5 is required but current is lvl 4. The point is the level of relation with any civ should be easily visible at diplomatic screen.
5. There should be notifications when one civ goes into a war with another. Checking graphs all the time is annoying.
6. It should be possible to rename a core world.
7. In tech tree screen, researched techs should be better distinguished from those that can be researched at this moment. Something like green border will do, i think.
8. AI civs seem to be quite passive at least up to the beginning of the late game. Wars are very rare (at least in my game) and alliances practically never happen. Most of the time ai civs will beg me to go to war with some other civs, they are afraid to fight themeselves. And when I do go to war on their behalf, they still won't declare war. I play on genius difficulty by the way. Or another example - my civ is very influential and starts to absorb planets of another civ that has higher military rating than me, what do they do ? Nothing. So AI should be more decisive and aggressive, I think to keep the game interesting.
Alliances should probably be available much earlier in the game and utilized by AI.
9. Exploration could be made more interesting. For example, we could have points of interest\anomalies on planets that can be investigated by flag ships. After all planets are huge and are likely to have ruins of old civs\crushed ships etc. It would certainly add more variety, because as of now artifacts\junk\capsules in space quickly become predictable and repeatitive. Also, exploration could use chain of events in addition to one-time events. Like when you trigger an event, and then go around gathering clues to progress down the line and in the end you get a major reward. Maybe something akin to archeology system in stellaris would also be very cool.
10. Precursor protection field module is somewhat overpowered, I believe. +50 % to evasion, shields and armor for a whole fleet is a bit too much.
Now, to some bugs i've encountered so far:
1. I had a bug several times, when ship icons on the bottom of the fleet were not visible.
2. Artifcat that is supposed to boost damage by + 2 (energy or kinetic) doesn't add visibly that damage when used.
3. Every time i choose to dissect artifact with a monster to get boost in science, the opposite seemingly happens and my current science gets reduced.
4. Diversity trait in egalitariansim tree says that citizens increase influence by 2 % for every social point. In reality they increase it by 1 %.
If I encounter other things that need attention (in my opinion) or bugs, i'll update the post.
5. Probably not a bug, but the cost of utopia dream tech obtained from the last perk in egalitarianism tradition tree is waaay too high. With ~400 science per turn it would take me 38 turns to finish the research.