Look, I totally get the struggle with the EF-RF adapter. I hauled my 5D Mark IV all over Europe for a decade before switching to the R6. The first time I tried using my old EF glass on the R6 with that adapter, it just felt front-heavy and awkward while walking through narrow streets. If you want one lens that never comes off for a trip to Italy, you should look at these two based on my time with the system. 1. Canon RF 24-105mm f/4L IS USM
This is what I ended up keeping on my camera 90% of the time now. It fits your budget perfectly and the image quality is honestly stellar for a zoom.

• Constant f/4 aperture means you dont lose light when you zoom in for a tight shot of a statue or a face across a cafe.
• The weather sealing is legit. It saved me during a random downpour in Rome and I didnt have to baby it.
• Nano USM focus is near-instant and dead silent which is nice for candid street shots. 2. Canon RF 24-240mm f/4-6.3 IS USM

I bought this one for a trip to the coast because I wanted more reach for architectural details without carrying a bag.

• The range is incredible for travel. You can go from a wide street view to a tight detail on a cathedral tower in a second.
• It isnt an L-series lens tho, so you lose that constant aperture and some sharpness at the edges compared to the f/4.
• Its way lighter than carrying two lenses, but that f/6.3 at the long end can be tough once the sun starts setting in the piazza. For Italy, the 24-105mm L is probably the smarter play. Its built like a tank and handles the R6 sensor beautifully without feeling like a total brick in your hands.