How to delete all email from Gmail and keeping them in Mail on my Mac?

Sorry for this question which I see it is recurrent but I am really lost. I switched from gmail to another (more privacy friendly) provider. I am keeping my gmail account active only to keep people updated about my new email address.

So it went full and I don't see any point in paying for extra space.

What's my goal, the one I am asking for help: I want to download all my email on my Mac via Mail and keeping them on my computer as a searchable archive (as Mail offers me to do). At the same time I want to delete all of them from the server.

Basically I want to find them in my Mail app but I want to see my Gmail empty when browsing it on line (web interface).

Unfortunately at the moment if I cancel just one, it happens the same on my Mail.

Anyone wiling to help out there? Thanks in advance

NP