As far as finding the irregular markers (threat 1, 2, 3) its pretty hit or miss they do seem to be more common in anarchy/war systems. I think I found another way. I went to an anarchy system that was industrial economy (I don't think the industrial economy matters in this scenario but I want to be specific) so I was browsing the missions at a star base and I came across a mission titled "Seize the Lazarus from a hidden cache" it is an illegal mission but I did not incur a bounty during it. It brought me to a irregular markers threat 1 on a planet in that system. I landed to find 3 shipping containers full of push and also weapon schematics. I gathered ~15 Push and ~5 weapon schematics. No enemies spawned but even if there were the SRV destroys them anyway haha. I did use a surface scanner to locate the irregular marker for the mission not sure if its needed but just in case I would grab one (surface scanners may be standard now I don't remember). I hope this helps people find more push because I spent way more time than was needed haha.
This has not been extensively tested but it seems pretty solid since it is utilizing a mission. The exact system I did this in was Huiche System however I feel Push is related to system states so it probably changes depending on the state of the system.
Source: https://www.reddit.com/r/EliteDangerous/comments/rht4rx/irregular_markers_and_finding_push/