Solved

Championship

Yes, it really looks like the league you're in in general and all leagues with your current tier being full are not showing up in the suggestion list, because in both cases it's not a viable league to join.

Edit: That said, I do think that the suggestion list and filter are broken. The system still prefers to show leagues that have absolutely nothing in common with the set filters over leagues that would match perfectly or are at least a way better match than the leagues shown.

No, I worded it misleading. I meant the league a player is currently a member of won't show up as a suggestion in a search of that player. That tool only shows other leagues, not the own.

Edit: Hope it's better now, the post above was meant as a reply to Joshua. That double post protection is a bit of a nuisance if it comes to edit in quotes afterwards.

I see. Also since you've got a free spot in Elite now I could try it myself setting the filters to match your league. Your league did not show up. At least searching by name works though, so your league seems to be fine.

But 3 out of 6 leagues shown had a race on Saturday and 6 out of 6 raced at the wrong time, up to 10 hours off even (race length and speed filters are still missing). The only thing that seemed to work was 2 car leagues only. So what's still broken seems to be the filtering of the list and/or the system selecting the leagues for the suggestion list. Maybe the pool/list of leagues the game uses is by far too small to produce any meaningful results.