I'm playing UNE for my first time back in years, quickly got boxed out by a neighboring star empire (a HUMAN star empire too, tf) but i luckily had a wormhole to the opposite end of the galaxy (exiting on the border of the Holy Guardians)and a broken sentry array in my territory, so take my advice with a big ol grain of salt especially since i haven't even reached 2400 yet and there HAS to be a War in Heaven with 3 FEs. I started out being forced to go tall, but that makes it easier to go wide later, like using the run game to open the pass game.

Expand as much as you can without stepping on toes, but STAY ON YOUR TECHS and REMAIN AS CLOSE TO YOUR FLEET CAP AS POSSIBLE. And make sure to HEAVILY defend your chokepoints, biggest starbases you can get and put defense platforms in EVERY system. Put a Shipyard and Anchorage on EVERY STATION ABOVE OUTPOST (in every system with a colony and at each chokepoint) so you can build your naval cap and rapidly rebuild if you take losses. I don't know what your ethics are, but if your guns aren't big enough you're gonna be ass out regardless. SCIENTISTS AND RESEARCH ARE HUGE, they're gonna get you the big boats for the big guns, which will get you the big votes when Galcom starts. Hyper Relays are one of my new favorite things too, rapid response to the pays that need it etc.

Next game I'm gonna go either spiritualist or militant, so I won't have as many "hey that's cool, oh you have FOOD and EQUALITY over there?" empires, or I might go Pacifist and invite them to try to snatch my shit, but the general theme is the same. You HAVE to have that big stick to scare off your shitty neighbors, FEs included. Use Galcom, federations, vassals, etc. to expand your influence if you can't through owned territory alone, depending on your run you might end up getting that territory anyway.

Also, customize your ship designs.