Two routes, one built into Gmail and one through a desktop client, with the built in one carrying fifteen years better than people expect.

The built in route, Gmail's importer: in Gmail settings under Accounts and Import, the Import mail and contacts option takes the Yahoo address and fetches everything server to server, mail and contacts both, continuing to pull new Yahoo arrivals for thirty days after. Before starting it, one Yahoo side preparation: with two step verification on the Yahoo account, generate an app password in Yahoo Account Security and feed the importer that instead of the normal password, the requirement that stops most failed attempts. The import runs for days on a large mailbox, quietly and resumably, landing everything with an import label. The one structural note: Yahoo folders arrive as labels of the same names, which is Gmail's model anyway.

The desktop client route for control: add both accounts over IMAP in Thunderbird or Outlook, Yahoo with that same app password, let Yahoo fully sync locally, then drag folders across to the Gmail account at your own pace with your own folder choices. Slower in wall clock, faster to verify since you watch counts per folder and the local Yahoo copy that results is itself a backup layer worth keeping on the disk.

Fifteen years favors starting the built in importer today, since it runs unattended, then spot verifying counts on the big folders afterwards, with the desktop route held as the surgical tool for anything the importer handled oddly. Once verified, redirect the daily flow: Yahoo forwarding to Gmail or simply the thirty day import window covering the transition while correspondents learn the new address, and the fading trust resolved by the mail existing in two places before it existed in one.