I'm currently playing a talish game on 2.2.3 (I'm way over my admin cap, but it is mostly districts, I'm still only possessing 29 systems, 25 of which I had within a few decades), and I haven't found any silver bullet for minerals past the early game. There is some ways that can help some though:
1. Perhaps somewhat obviously, build any and all mining districts available on whatever planets you do have. Gene mod your population with Communal (and/or Fertile if you went with the biological ascension path) rather than replacing mining districts with city districts. Also never sacrifice mining districts for agricultural or generator districts, that is what your ringworld is for ;-)
2. Mineral Purification Hubs (upgraded Mineral Purification Plants) will provide 2 extra miner jobs as well as a nice bonus to mineral production. That is essentially an extra mining district on each planet. Prioritize building them on planets with many mining districts, but eventually you will want one on every single planet you own, even if it has zero mining districts (excluding your Ringworld and Ecumenopolis, where the limited building slots are more valuable).
3. A Ministry of Production on every planet with CG/Alloy production will let you produce more CG/Alloys for the same amount of minerals.
4. Run the Consumer Benefits trade policy. Compared to Wealth Creation you are essentially trading for consumer gods at a rate of 2 EC per CG, which is crazy cheap.
5. The Production Targets and Ambition: Omnifarious Acquisition edicts can help a bit, but not that much. You are going to have to trade for minerals (and/or CG/Alloys, which amounts to the same thing), so reducing usage is always better than increasing production...
6. On that note, as soon as your CG consumped by pops (hover over the CG icon in the top bar to see this number) exceed about 40 start running the Recycling Campaign edict continuously. Depending on traits and living standards this should happen when your empire reaches somewhere between 50 and 100 pops.
7. As alluded to above you will probably want a Ringworld, and possibly an Ecumenopolis (if you have a largish planet without any mineral deposits), but don't bother with habitats. They have an alloys maintenance...