Q: Can Salesforce Integration Licenses access Standard Objects like Accounts and Opportunities?

A: Yes, but only with some configuration weirdness!

To access Standard Objects, a userid with a Salesforce Integration License must be assigned to the right kind of Permission Set: the Permission Set’s “License” field must be set to

• no specific License, or
• a “Salesforce API Integration” License:

• a Permission Set whose “License” field is “Salesforce” can’t be assigned to a userid with a Salesforce Integration License, and
• a Permission Set whose “License” field is “Salesforce Integration” can’t access Standard Objects.
• And a Salesforce Integration License’s Profile can’t access Standard Objects, either.

go figure.

thanks to Josh Dehkordi and Surya Kamkipati for their help sorting this out!