I accidentally deleted an important texting thread. How can I find out if it’s still in my iCloud back up and restore that thread?

You can restore your device from a backup, https://support.apple.com/en-us/HT204184

If you do NOT use messages in iCloud, your messages may be in your backup (provided the messages existed when you backed up).

ShNoRy Said:

"Any advice on how to restore an important text thread on my iPhone 13th?"

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What to Consider:

A. Restore from a Backup:

Restore your old iPhone from a backup of it that contains these messages, and you could recover them.

B. Check a App on Another Device:

If a messaging app (i.e. Messages) was enabled on any other iPhone or Apple computer, then check the Messages app on your Mac to see if it exists in it. You'd start up your Mac, not connecting to the Internet, and open the Massages app. Then proceed from there with retrieving it. Important: Be certain you do not connect to the Internet while booting up, as syncing would delete it. So, power off your routerto avoid the connection.

C. Learn to Back Up:

If you have no backup of your iPhone, then take this as a learning experience, knowing to always backup your devices, every-so-often. That way, you and recover from the backup should anything like this go working in the future.