You can still use booking. You just don’t need to do the booking via booking. Most Hotels have their own Homepage. Just book from them. It’s cheaper anyway. For Airbnb I see no real alternative. You might search for camping places via your preffered map app. They are often not listed on either platform.

Banking worked once I added a Google account to microg. Which is not the best I know, but thats a compromise for now. With e/os and others you also habe to keep in mind that not all images allow you to lock your bootloader.