You would need to have had iOS 16 or later on your iPhone to be able to recover deleted messages and conversations.
Then, you can only recover messages and conversations that you deleted within the last 30 to 40 days.
If you have iOS16, see: Delete and recover messages on your iPhone or iPad - Apple Support
Seems, for iOS 15 and earlier, the option to recover deleted Messages is not yet available,
ie: you can only recover deleted messages from a back-up of your iPhone.
You may be able to have any important messages that were deleted, re-sent by the sender.