EDIT: false alarm, it turns out - the solution below worked only the first time after reboot; once OpenCamera was backgrounded, and then opened again to take a new picture - upon the tap on the last photo taken thumbnail, I got the old stock gallery (with all its problems) again :(
Ok, here first I found:
There's no way to automatically download and save sent media from whatsapp web to mobile.
But there's a workaround
You need two mobile numbers and the ability to run two whatsapp accounts either using a built in dual account feature if available or using a third party dual app provider to achieve this (for a second mobile number, there are several apps like ...
Data store by the gallery apps are thumbnails it generates to preview the pictures and videos. The Gallery app can be considered as a movie theater where you go to watch a movie (in your case, viewing picture and videos in your phone). If its goes bankrupt (in your case deleting its data), it won't stop you from going to another movie theater.
Yes, Google Photos does send it to the bin.
You can prevent this from happening by tapping the "Free up space" feature in Google Photos, which will delete all the photos on your phone that have already been backed up to Google Photos.