As to why fwupdmgr didn’t find your update: note that of all framework updates:
https://fwupd.org/lvfs/search?value=framework
only the Ryzen 7040 is listed as “stable” for its state. All the other updates are in “testing” state. By default fwupdmgr won’t look in the testing stream. You need to activate that explicitly. This is unexpected because normally you’d expect an update to move from “testing” to “stable” once the update goes out of “beta”. Framework didn’t do that with most of their updates.
[EDIT: I see in your screenshots that you did have testing activated. Leaving this comment here for posterity, since this is something other people will likely stumble over until Framework gets the confidence to push updates to stable]