Gmail needs an App Password (not your normal password) with 2-Step Verification on, and IMAP enabled in Gmail settings. Create an app password →
Signature
Type or paste your signature. If you have signature HTML code, click "Edit HTML" and paste it there. Added to new messages, replies, and forwards from this account.
Sorting rules
Add a rule
Emails that match will move to the folder you choose — automatically, from then on.