We've already found that the system factors in your previous missions to influence the new missions available. The more you run metal missions the more rare they will become.
Do your tests again but only run fabric missions for a week and the see how rare your metal missions are then.
You missed where I said that I did not run any missions. I recorded what was available, stepped onto my ship, recorded what was available, stepped off my ship ... and repeated that cycle. I didn't actually run one of the 3000 missions I recorded, so if this effect you claim has been demonstrated exists, it had no influence over my results.
Given how few missions there are to run, I can see how it would seem that "less" metal missions are appearing. The fact is that there are a set list of missions. All but one grade have fewer metals missions than you can send your full crew out on. If you manage to send out 3 companions on the only 3 Grade 3 metals missions that there are, then of course you are not going to see any more metal missions until any of them have finished. But given how little the devs care to track anything beyond the variables they are now tracking, it just does not make sense that the act of running ANY sort of mission means it will appear less frequently in the future and that, furthermore, if you stop running a certain type of mission it will increase the odds of those missions appearing. What you are suggesting would require that the game tracks 96 separate variables (there are that many UWT missions per faction, including the Mission Discovery ones) and constantly compare the ratios of Gift to Fabric to Metal missions to determine how to skew the results the next time you randomize your mission list.
Now, do you really think the developers of this game would put so much nuance into a mission selection system when they haven't bothered to manage a simple two-variable system that could track how many consecutive fails you have REing a particular item and curving your chance of learning a new schematic? Track 96 variables per character when they won't even track 2? Does that really make any sense? Or does it make more sense that there is a fixed probability for any given mission in a list of a fixed size and that they altered the odds to favor one type over another? They can alter the odds without having to track a single variable.