Assuming that you are using iOS 16.x, the option to tap Edit and then select Show Recently Deleted will not even appear unless there are messages that have been deleted within the last 30 days.
As a test, delete a recent message that is not that important to you.
Tap Edit, then Show Recently Deleted will now appear, so you can now see the message that you just deleted, along with an option to Recover the message.
Note that any messages in Show Recently Deleted will be automatically and permanently deleted after 30-33 days.