Is there a service that rates app security/permissions?
There's one called Exodus Privacy which has both app (open source) and website https://exodus-privacy.eu.org/en/page/what/
One downside: it scans only apps available on Google Play, you can't upload apk manually.

Here's an example of it's report on one of popular browsers:
https://reports.exodus-privacy.eu.org/en/reports/50316/

(Click on image to enlarge it)



I prefer to use it together with Yalp Store app (free and open source) which allows you to download apps from Play Store without google account and services and has built in support of Exodus Privacy on app's install/update page: