I can’t change my Apple ID profile picture

Try a restart.

Restart your iPhone, iPad, or iPod touch

Try a forced restart.

Reset Device

If necessary

Hard reset

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

Restore to Factory setting

Backup - Restore your device from an iCloud or iTunes backup

If you go to Settings/Your Name/iCloud and tap your profile picture, what happens? Do you see Edit on the picture?