Top budget-friendly zoom lenses for Canon RF mount systems?

Honestly Im about at my wits end with this whole switch to mirrorless. I saved up for months to get my Canon R6 mark ii thinking it would be this massive upgrade from my old Rebel but man the lens prices are absolutely killing me right now. I feel like Canon is just gatekeeping all the good glass behind that red ring and I simply dont have four thousand dollars to drop on a couple of lenses. I tried using the EF to RF adapter with my old 75-300mm but the autofocus is just... its bad. Its hunting constantly and the whole setup feels so front heavy and awkward to hold during my sons baseball games here in Ohio.

I just want something that actually fits the mount natively without breaking the bank or requiring a second mortgage. I have a trip to Yellowstone coming up in like three weeks and I really need a decent zoom but every time I look online its either a cheap kit lens that feels like a toy or a professional lens that costs more than my car. Is there actually anything halfway decent in the RF lineup that isnt three grand? Im looking to spend maybe 700 or 800 bucks max which I know isnt a ton in the photography world but it should buy something better than what I have now right?

• is the 100-400 f5.6-8 any good or is it too slow in real life
• what about that 24-240 all in one lens for travel
• are there any third party options i missed

Are the non-L zooms actually worth the money or am I just gonna be disappointed again? I really dont want to have to sell this body and switch to Sony just to get some affordable Tamron or Sigma glass but if I cant find a zoom that works for a normal persons budget I might have to. What are you guys actually using that doesnt cost a fortune?