Am I correctly replacing 2 x two-pole breakers with a quadraplex breaker?
Sure, if it fits
Your panel labeling specifically lists the BQC type breaker, so that's alright.
Your wiring (one pair in middle, one pair outside) is correct.
The breaker appears to be &quot;common trip, both inside and outside&quot; so that is either correct or overkill for your circuit, so that's fine.   (Beware Eaton &quot;Non-common-trip&quot; types).
However, your panel is labeled for BQC breakers only in certain places depending on whether the bus stabs have a forked tongue.  The label is not specific as to where that is in your panel, but given that it's a 30-space panel and the old CTL limits were 40-space, I'm guessing it's the bottom 5 rows of spaces.  Which are mostly populated already.
Might be time for a subpanel
As you are seeing, 30 spaces/40 circuits is inadequate for a modern house.  A better use of 2 spaces might be to feed a subpanel, so you can offload some loads into that.
If you had any thought to having a &quot;critical loads&quot; subpanel to support future generator or battery/gen/solar backup system, this would be a good time to think about that.
Normally I recommend a house finish with about 50 spaces, so by that a 12-space subpanel would suffice; however, since your house is so full already, I'd aim for more like 60, suggesting a 24-space or 30-space subpanel.  Scrimping on spaces is a futile gesture; the price difference is tiny compared to the frustration of - well, you know exactly, don't you!  You spent more on that BQC breaker than the price difference would've been for the last guy to buy a 40-space panel instead of the 30. So why not? Spaces are cheap, make the sub a 40-space. Never run out of spaces again.