Can deleted messages on Messenger or Discord be recovered from backups or server logs?
Hey mighty.trail, welcome! Great question.
For us regular folks, once a message is deleted, it’s pretty much sent to the digital void. 
You can’t ask Discord or Meta for server logs.
The only “trick” is on Discord, where some servers use logging bots to record everything. Or, some people use client mods to save messages locally, but be warned: that’s against Discord’s rules and can be risky for your account!
For Messenger, your only hope is if someone took a screenshot. 