I have never read that about waiting until 3000 rounds. That does not sound right, so a source of that info would be welcome if you can post that, thanks.
On the Anschutz website they have a page about cleaning, link here (two languages, German and English, look top right for the button for language version):
https://www.anschuetz-sport.com/en/wie-reinige-ich-mein-gewehr/
The first sentence says: "
In order to ensure consistent precision over the long term, it is essential to clean the rifle regularly after shooting".
It also has warnings about leaving solvents in the barrel for too long. However the article lacks specifics. It does not have enough information for a thorough barrel cleaning system IMO.
The Anschutz USA website has a page on cleaning bolts and magazines, but I could not find any article there for barrel cleaning, link:
https://www.anschutznorthamerica.com/maintenance-tips.html
RE ammo: Those brands you listed are not target quality for consistency, except for maybe CCI Standard Velocity in some rifles. My European rimfires (Anschutz and CZ) don't seem to like North American rimfire ammo, so I rejected CCI a long time ago for target grade, and only use it for plinking. I think you will find your Anschutz will like the European ammo brands SK, Lapua, Eley, RWS. I have not tried the Norma Match grade ammo yet. I shot one box of Norma Tac and it was OK, but with the wind variables that day I cannot say if the Anschutz likes it or not. I doubt you will find any supersonic ammo to shoot consistently accurately. All the target grade ammo I am aware of is subsonic.