I was able to solve my own issue:
I noticed that the settings contained more configuration options which have definitely not been available directly after updating Postman to the latest version. (I created a screenshot.)
The configuration options now contain a “Working directory” and a setting “Allow reading files outside working directory”.
My certificate file was located outside of the working directory. Enabling the option did not change anything, though. The file was not read. (Access rights are correct.)
Only after copying the p12 file into the working directory of Postman and re-configuring the certificate with the new path, the client certificate was use.
So, my problem is solved. But maybe somebody would like to check:
a) Why wasn’t the setting available immediately?
b) Why is the setting “Allow reading files outside of the working directory” not working as expected?