Transfer Signal using Signal-native Backup and Restore
The best source to install Signal is always direct from the website https://signal.org/android/apk/#target
On the old phone
On the new phone
Starting Signal the first time, it asks you if you want to set it up newly or restore from a backup.
On the next screen you will be asked if to restore from another device or from a file. Chose the latter:
On the next screen click the button "Choose backup":
This opens the native Android file chooser. With the button top left you can switch between internal storage and memory card.
Choose your backup file.