Switching the 'Page Type' / fieldset after page been created

Hi, if I've got this right - that initial 'Page Type' modal when you create a page is the point at which you assign a fieldset to a page.

But what if, after some work, there's a change of plan and you want to give that content a different fieldset, or a new one - is there a way to do this in the CP?

It seems Collections have this option when editing where you assign them a fieldset via a select menu - but not pages.

Can you only do this for pages by editing the .yaml files?

Many thanks!