Folders in (Text) Messages App

I’m curious if it is possible to create folders to move messages from specific conversations, other than archived or spam/blocked? As the subject of the thread states, this is for the (text) Messages App, using the standard up to date OS on a Fairphone 4.

Any help is appreciated!

Not possible as far as I know in the standard app.
Bear in mind that SMS is designed for brief near-real-time conversations, not for long-term conservation.
Alternative apps may offer to copy content.
You can use an app such as MyPhoneExplorer to export SMS and then manage the content according to your needs.