@crabladyanne Sorry, not at all.
For the time being, leave your gmail account the way it is, except activate "Download Messages for Offline viewing and searching" Do not yet select "Take account Offline."
Leave Vivaldi and the mail client OPEN and running for several days until you have verified, by spot-checking if nothing else, That the body/contents of every single one of your emails has been downloaded to your current copy of Vivaldi (in the alternative, you could do all of this with a new, standalone installation of Vivaldi that you do not intend to use for browsing all the time.)
After you are SURE all of your emails are fully downloaded - not just the list of mails but the contents of each individual mail as well, THEN you can take the account off line and remove the server settings so that it will not accidentally hook up to the server. This is now your archived copy of all your mails to date. You can reference it off line at any time.
Once that is done, use a different instance of Vivaldi with a fully functioning email client. This will allow you to keep up with your current mail flow. In that instance of Vivaldi, or using the web interface of GMail, you can now delete emails that you do not have a current need to interact with, keeping only those which you feel you may need to refer to on a daily basis, reply to, forward to others, etc.
Your disconnected version of Vivaldi is your archive. Your connected version is your working platform.
At least, if I were in your position and just wanted to archive years of mail and still make more room in my gmail account without having to buy storage space, that's what I would do.