Can I connect a 15A surge protector to a 13A extension cord?
Provided what I’m plugging in (a laptop drawing relatively little power) doesn’t exceed the extension cord rating, there should be no issue.


This is correct. If your load is well under 13A, you shouldn't see any issues. 

The obvious counterargument is that with this setup, the 13A extension cord could fail before the surge protector kicks in to protect the system. Like, with a 14A load. So, generally, your setup is not recommended, especially for a long-term installation.