Interchangable compatablity of circuit breaker brands
Short version: you can't cross breaker brands.   You cannot put a competitor breaker type in this panel.
A &quot;tandem&quot; breaker is not what you want.  Here is an article about those.
What you're hoping to use is a THQP breaker, which appears very similar to a tandem breaker, however, is actually a 2-pole breaker that is half-height.  On certain GE panels, GE has a system that uses 1/2&quot; tall (half-height) breakers, 2 per breaker space.  Their 2-pole breakers in that system are 1&quot; tall and straddle 2 breaker spaces, with a 1/2&quot; breaker above and below them.
You can't use them.  Those half-width breakers clip onto a special cross-bars added to the bus stabs, and your bus stabs don't have them.    You can see the cross-bars in the lower 5 rows of this panel here: