I haven't had a go on messages yet, a quick search on the internet shows some tutorials on restoring messages from icloud/itunes backup. Some ways will 'restore' your complete phone alongside restoring the messages.
This link lists a number of option: https://www.businessinsider.com/how-to-recover-deleted-text-messages-on-iphone?r=US&IR=T.
However, I think the problem with the messages app is that you may not be able to delete it at all: https://discussions.apple.com/thread/252164318
My problem was not limited to the messages app, almost anything that gave notification stopped after my IOS 14 update.
The reason I started this delete and new install approach is that I noticed when I installed a new app to manage my gmail mails, that app happily gave me notifications, the mail app (non-Apple) on the phone when I updated to IOS 14 stopped doing so. Moving on to WhatsApp, which seemed safe because of the backup feature, was also successful.
Not having notifications from Eufy security when 'visitors' are detected with my home camera system was one of my bigger problems. What's the point of having a camera based security system without notifications? Also here a delete/re-install was succesful.