Some further thoughts and observations - and I'm kind of thinking aloud here, so apologies if any of this is wrong or obvious. Probably much of it you've already figured, but it doesn't hurt to spell it all out in detail:
In the early game, you need loads and loads of minerals. So you have to build loads of mining stations and/or mines. These cost energy in upkeep, so suddenly you have a huge demand for energy in order to feed your mine-building. Energy resource locations seem to pop up at most at the same frequency as mineral deposits (in my experience actually significantly less often, but possibly that's just Sod's Law), all of the mines cost you upkeep in energy, and you only need the energy for that upkeep whereas you need minerals in order to build any of the mines, and all of that together seems to mean that unless you're either very clever or very lucky, in the early-mid game, you'll be desparately struggling to break-even in energy as you amass a steadily growing surplus of minerals.
Eventually you'll have built all the mineral mining stations possible and gotten a fair amount of planetary infrastructure, so unless you go on a big fleet-building exercise (which to my mind is what you do with your profits, rather than part of your standard overhead) your need for energy credits will stabilise, and finally at this point, if your colonisation/territorial expansion has gone well, you'll be able to gradually achieve a decent energy income. In my experience this is mainly through spamming power plants on my colonies, which should have grown nicely by now. Unfortunately, because you at first seem to have such a desparate and insatiable need for more energy, and because there's often a significant lag between ordering capacity and having it come online, it won't be long before you suddenly have far more energy than you know what to do with.
And until you unlock terraforming in the mid-late game, you have pretty much nothing to spend it on, besides indulgent diplomatic deals, but even then it can be a struggle to dispose of your surplus. At this stage it seems extremely easy to reach your energy cap. Making extensive use of robots can help, but sometimes that isn't enough, and some civs won't even have access to them.
You now have plenty of (or too much) energy, you can support a large fleet maintenance cost, so now you want to start churning out fleets and want more minerals. But you've already built all the mining stations you can, so your only options are conquest and fine-tuning your ratio of power plants to mines on your planets. In my experience, in large empires, your credit income can start to swing quite wildly at this point depending on what your sectors are doing - the sector AI seems pretty erratic to me, but maybe I'm just not microing enough (although doesn't that defeat the purpose of the sector AI?). It also seems unbalanced the way that temporarily going over your cap (e.g. to nurse a new colony before handing it over to the sector governor), can have a dramatic effect on your income, swinging you sometimes from a huge surplus into deficit - only avoidable by wasting influence doing micro-intensive gymnastics swapping things back and forth into and out of sectors.
Now possibly my experience or my playstyle aren't typical, but if they are...that's looking to me like a fairly dysfunctional economic system - lurching desparately from one scarcity to another and then suddenly to a superabundance you can't even make any use of, and then back to mineral scarcity with few options to resolve it.
Honestly, my worry is that the flaw's a fundamental one rather than a question of tweaking the balancing, and to do with the very fact that you have one resource which is all fixed costs with no variable (besides terraforming which is lategame-ish and extortionately expensive (plus, as you noted, the strategic resources for it can be impossible to find)) and the other being all variable and no fixed costs. Unfortunately I think that's as far as my intuition can go without having to do some equations or draw a diagram or something. I also worry that the conflation of 'energy' as a resource, and the 'energy credit' as a unit of currency is causing a huge conceptual, thematic and economic mess.
Phew...that ended up a lot longer than I'd planned. Hope I'm not barking up the wrong tree with all of this!
The other thought I had, which is somewhat tangential to all that, and which I'm not certain where directly to go with, but: is one of the issues the fact that mining station output seems pretty much fixed, and afaik isn't modified either by any tech or by any of the ideological/governmental/racial bonuses? Was coming up a lot in another thread about ethic/government/trait balance (
https://forum.paradoxplaza.com/foru...uide-to-ethics-traits-and-governments.926557/ ). Not certain if there's an easy answer to that which avoids causing more problems than it solves, but it's probably worth thinking about.
Sorry for the wall of text. Hope some of it is helpful! Didn't add anything about influence because probably all the issues with it are all just too plain and obvious.