My answer to this is a two-parter, because I believe the two issues are intrinsically linked.
The first is that combat is very meh. While I like watching the little battles (they are quite pretty), and there is some element of rock-paper-scissors going on in terms of recognizing that an enemy is using a particular weapon and then attempting to counter it utilizing the ship designer/upgrades... honestly the whole thing pretty much comes down to building lots of ships with a thin veneer of choice laid on top. There's a lot of different ways to tackle this problem, but a few suggestions;
1) Impose an 'efficiency' loss on fleets. Rather than having an empire naval cap, have a cap for individual fleets. That number can change based on technologies and admiral skill level. Fleets that go beyond their cap start to suffer reduced speed/firing speed/dodge, effectively simulating command and control problems as the number of moving parts increases. Fleets above that limit also start to cost more to maintain, as logistical needs swell beyond efficiency. In order to dissuade multiple-fleet stacking, a slightly modified efficiency loss should be imposed.
(As a very loose example, treat the 'combined fleet cap' as 75% of the added-together caps of each present fleet. So if you have a fleets with individual caps of 32,33,and 34, and these fleets fight together, the combined-fleet cap would be 32+33+34(100) * 0.75. So 75. If all three fleets combined have >75 ships, then all fleets suffer both their own individual penalties, as well as the combined-fleet efficiency penalties. Hopefully that made sense.)
2) Allow high-level commands for fleets. Completely losing control of fleets during combat takes some of the fun out of it and is occasionally frustrating. I'd like to be able to set fleets to act offensively (actively close and/or maintain ideal distance, giving chase if necessary), defensively (ships will maintain their current position and only engage when enemy ships are either within weapons range, or are actively being targeted by enemy ships), and withdraw (ships actively move away from the enemy in an attempt to escape weapons range). The default for fleets would be Offensive, though you should be able to change that default. Also, you should only be able to give one order per battle, to avoid rewarding(and thus requiring) micro-intensive strategies. Battle would begin in the fleet's default state, and you could adjust it once and only once.
(Obviously the current weapons were not designed with this in mind and balance could be a problem, I accept that as a flaw. But it's not insurmountable.)
The other thing that needs to change is the economy. I don't even want to get deep into this, but on a player-enjoyment level, I am still not remotely satisfied with Minerals + Energy, nor am I satisfied with a universal bank where all produced minerals/energy are made instantly available. Nor am I satisfied with the lack of industry as a mechanic, where structures, stations, and ships are all basically produced at the same rate regardless of where they are, with the minor exception of modifiers from leaders/modules. But I accept that I'm probably not going to see *major* changes to all of that.
On a mechanics level, though, the lack of industry essentially transforms minerals into industry, and because the current combat system basically translates ship numbers into combat success, who wins a war basically comes down to who is producing more minerals, and mineral production is fairly linearly gated by energy production. So, y'know, all you do is constantly balance your energy with available mineral production, and you have more or less everything you need to win wars.
It's just too simple. It looks simple, it feels simple, and its results are simple. It needs complexity, it needs variables, it needs obstacles.
One humble suggestion that may not actually fix the overall problem as I see it, but might help both inject some life into the economy as well as have an impact on how fleet warfare plays out;
Split minerals into 'metals' and 'rare minerals.' Metals would be fairly common and would be best described as providing the 'structure' of ships. The metal cost of a ship/base is determined first by its hull class, and is adjusted largely by armor based on level and component size. Heavily armored ships, especially large ships, would cost large amounts of metals. Meanwhile, Rare Minerals would be rarer in the galaxy, more expensive in terms of energy cost-per-unit, and are used to construct the components of ships. Different ship components use different amounts of rare minerals, particularly higher level components and larger sizes, would cost quite a bit more rare minerals.
This would separate ship sizes from ship technology level in an important way. It might not be feasible for an empire with access to rare minerals but not a huge amount of metal, to build large, technologically advanced ships, at least not en-masse. It might make more sense to build smaller, better-equipped ships that actually have a chance of competing with bigger, less well-equipped ships produced by an empire with large amounts of metal but not much in the way of rare minerals.
It would provide incentive to continue using older tech, because production and access to materials wouldn't scale so linearly. Currently there is no reason to not use the best tech available.