For this to work, the OS version you install should match the OS version the restored backup is from.
Since you didn’t specify which OS and which version of it ran on the phone, we can’t be sure of that.
The guide links to the install file of the most recent 19.11.2 version of Fairphone OS, which is the best guess in such a situation, but if you are certain it was an older version or just want to try, older Fairphone OS versions are being kept available here … https://support.fairphone.com/hc/en-us/articles/213290023
I’m thinking of a different approach now, though.
The backup is restored, the data you require should be there, but the phone doesn’t boot to let you have a look.
TWRP can access the restored files on the phone, so the file in question could be copied to a computer.
Question is: Which file contains the call log, and is there a way to make sense of the file’s contents on a computer?
Perhaps somebody else here has already done this before?
No, I can’t think of a simple restore of a backup doing that.
It is actually not that easy to get the Fairphone 2 into an unsalvageable state.
As long as Fastboot mode works, you will have options, here’s one … (which doesn’t help with accessing the call log just now, because it deletes user data) …