I bought the Ozmo 950 for 380 EUR:
https://www.amazon.de/gp/product/B08D9R15DC/ref=ppx_yo_dt_b_asin_title_o02_s01?ie=UTF8&psc=1 not sure if that's an option.
Has mopping, Lidar, app is okay so far. You can enable advanced so it drives around and sets up rooms, then you can mark rooms it may and may not go to, it detects rooms as well and you can send it to a specific room, or say it should clean a specific area. It has messed up once in about 15 cleanings in terms of finding its way back to the charging station the first time I enabled advanced mode, not sure why, after that it was fine.
I am using:
https://www.amazon.de/gp/product/B08TVP444T/ref=ppx_yo_dt_b_asin_title_o05_s00?ie=UTF8&psc=1 as a cleaning agent after searching quite a bit to make sure I find a cheapish one that will not damage the robot while still being good. This has a slight fragrance, think the bottle will probably last me two months tbh, my apartment is about half the tank of water since most of it is wooden floor so robot only does a very thin layer, and I run every second day on a schedule.
I specifically got it instead of the cheaper ones since I wanted mopping.
Your budget is lowish, so do be careful that you end up not only with LDR but also room mapping, specifically talking about the older roborocks. note the E4 says it is not random, but it most likely will end up random, you're already paying half the price just in import, so do consider that when purchasing.
Having a robot vacuum cleaner doesn't really save that much time if small apartment, personally I got it because of the mopping function, I could probably have vacuumed as quickly and often as the robot without that much time difference. If you are looking at a large house, then you should probably think about the size of the bin in the vacuum cleaner, you're probably going to empty it often, so might not be worth either.
EDIT:
I do think within the next two years we'll see a lot more cheaper good vacuum cleaners come out since the tech for camera in front is maturing, that should make navigation a lot better as currently things like driving cabling it doesn't properly understand for non-camera.