if you do not download some really obscure note taking app from the playstore, then yes you will be fine.
You can try the standard notes app. It is what i decided on, after a lot of recommendations. It is open souurce and they say they have been audited.
It does allow end-to-end encrypted online storage, but can be used offline without internet permissions just fine. I use the free version but there are paid features, i dont know if free version is enough for what you need (https://standardnotes.com/ https://play.google.com/store/apps/details?id=com.standardnotes)
I think AppVerifier explains it themself best:
https://github.com/soupslurpr/AppVerifier
AppVerifier is an app signing certificate hash viewer and verifier.
It enables you to easily verify that your apps are genuine with others!
AppVerifier takes the app's package name and signing certificates hash(es) and compares them to the ones you provided or the ones in the internal database to verify that your apps are genuine.
You can simply share the verification info to others and receive verification info from them and share the received verification info to AppVerifier and you will see the verification status.
AppVerifier does the heavy lifting for you
So it is a tool to protect you from getting the wrong version/ a maliciouse version of an app. It does nothing to make sure that the app itself is malicouse tho (because it is not possible like this)
But honestly it wasnt really a good recommendation on my part, since it is mostly used by people, which download apks from github etc. or obtainium.
(but ofc it can also be used for app store apps)