Ue their infrastructure for searching and then, call the place you wanna book

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.

Sooo, it is not as convenient, but I usually search for ho(s)tel/B&B/etc. on openstreetmap and then check their own website or call them directly when I found something in the correct area.

FairBnB

Home2Go (uses X payment provider)

HostelWorld

Vrbo (Expedia / Texas owned)

homestay.com

This site shows a lot of options : https://travelfreak.com/airbnb-alternative/

I used to browse traum-ferienwohnungen.de for Germany and Austria some years ago. But that seems to be owned by an Indian corporate which is backed by Airbnb and before that Axel Springer, what a clusterfuck: https://techcrunch.com/2019/05/01/airbnb-backed-oyo-moves-into-europe-acquires-leisure-from-axel-springer-for-415m/ So really not an option anymore.

Local rental agencies are usually good.

If you know what region you want to go to, look for a local tourism bureau website. Its often good enough these days and usually has offers from locals

hrs.com is german and has a similar world offer like booking.com