Otherwise: for ~20 years now I've been able to just attach two imap accounts in thunderbird, and drag to move/copy everything from one to the other, and that'll just chug away until it's done. I've never had an issue doing that.
I have used Thunderbird for everything, set to download everything and never delete, so had my primary backup there. I take regular backups of the profile directory as secondary measure, which are kept on my NAS and offsite.
What I did was to just decide to do a hard break. I renamed the old IMAP accounts, added the Proton Mail accounts using the IMAP bridge, and then configured my DNS to point to Proton.
DMARC and all that was easily set up as well thanks to Proton having nice guides and active verification.
Now I still have access to my old mail in my old account folder, and I can use the Proton Mail app on my phone for new stuff.
I also migrated a secondary mail, which was not using my domain and which I've had for almost three decades. There I had to do the laborious task of changing any accounts tied to it, and notify people still using it. I've been keeping it operational for a year and still get the occasional mail, but at a point where I'll be retiring it soon.
Overall been very happy. It showed me it was easier than I feared as long as I have Thunderbird and mail accounts under my own domain.
Moving the mails was as simple as ctrl+a and dragging my mouse in thunderbird.
Between providers with a custom domain (zoho to mxroute) was easy. Just updating the DNS records and moving the emails.
If you are technically able (really just buying a domain and setting the DNS records the provider tells you) I would recommend getting a custom domain. It gives you the ability to move providers at will pretty easily, even if you did want to stick with a gmail for now.
Should be sufficient unless you lose your computer and your email account gets blocked at the same time.