Is there anything in Standard reporting or with a custom report type that will allow me to pull a report of profiles and related details. For example which profiles have access to which apps or which record types.

Hi Sara,

This wouldn't be possible by declarative  methods, there is an idea posted on the idea exchange for the feature.

https://trailblazer.salesforce.com/ideaView?id=08730000000glw0AAA

you can try using below AppExchange solutions to achieve this,

https://appexchange.salesforce.com/appxListingDetail?listingId=a0N300000016a4jEAA

https://appexchange.salesforce.com/appxListingDetail?listingId=a0N3A00000FeF99UAF