If I care about binary integrity, I wouldn't involve an app store. https://signal.org/android/apk/ is a perfectly cromulent way to get your hands on the APK file directly from the source.
How do you keep that updated? What if there is a security issue?
pull the apk from your phone with apktool. Compile Signal reproducibly with their instructions. Use the diff.py tool they provide and check for the message that confirms the APKs match.