iOS is more restrictive, but you can still retrieve older versions through your account history if your device is too old for the current update.
: To prevent the Google Play Store from automatically updating you back to the latest version, open the Play Store, search for Messenger, tap the three dots in the corner, and uncheck Enable auto-update . How to Download an Old Version of Messenger on iPhone (iOS)
: Software like AnyTrans can sometimes help you back up and restore specific app versions if you have them saved in an "App Library". Older versions of Messenger (Android) | Uptodown