Microsoft
MicrosoftHi jeroenstruik, thanks for the comment! I've responded to Stefan_Spinnler and Valyu above as well, so be sure to read those because i think it covers some of what you've mentioned here.
One of the solutions we are considering for the "saved on this site" tab confusion, is showing this tab by default on sites, like yours, with a large quantity of saved templates. This seems like it would alleviate the confusion so many of you are feeling with our change to a new tab, without getting rid of access to inspiring starting points for less developed sites.
As I mentioned in my reply to Stefan, I don't know why the "+New" button shows different options when you are on different site levels, but will ask around to see if there is a way we can standardize this logic/ offer this option in as many places as possible.
As far as pages being moved manually/ being more flexible pieces of a site, we are moving towards a document like treatment in many ways. One of the big ones is our new share experience where we have onboarded to the same experience as the rest of M365. There are other features we are working on to make the pages experience more doc like, so stay tuned!