Ok, if the amount of data is a problem, another option is to just download your mbox from Google takeout, treat it as an archive, and use something like notmuch to search your old mails. You can then store and backup the mbox anywhere you want.

In addition to the iCloud, I have a free ProtonMail account, which I use sparingly, and anything large or important that comes in there I move to local backup and delete. 99% of the messages I get can just be deleted. If you set up pop3 you can auto delete from the server. That’s the old school solution, but it depends on your use case. The pop3 option doesn’t work well with multiple devices.