It says I am signed out of my account on iMessage and won’t let me enter my password

What happens when you try to enter the password?

See the Apple Support article(s) below.

If you can’t turn on or sign in to iMessage or FaceTime.  *

Messages Troubleshooting.   -

Some things you can try. Do you have access to another WiFi network where you can try? That has worked for several people.

Try a restart.

Restart your iPhone   *

Restart your iPad.   *

Try a forced restart. See the section towards the end of the article.

Reset Device. -

If necessary

Hard reset.     -

Do a backup and try a factory reset. Then restore from the backup.

Restore to Factory setting.      *

Restore - If you see an error when you update or restore your iPhone, iPad, or iPod.   *

Backup - Restore your device from an iCloud or iTunes backup.