That Eaton breaker DOES NOT belong in that GE panel!
That's called an "alien breaker". The bus stabs on different makes of panel are different shape (to avoid patent infringement) and they will "clip in" but they won't work reliably. You can get a panel fire, which will at the very least burn up a bus stab, taking 2 spaces out of commission, which is the last thing you need when you're already having panel-cram problems.
GE does double-stuffing in a completely different way
Instead of a balky quadplex like the Eaton, GE uses special bus stabs which allow breakers to "straddle" spaces, leaving a half space on each side of them, which you fill with 120V half-width breakers. If you put those on each side of the breaker you have pictured, you'd have the equivalent of the Eaton quadplex.
The Eaton breaker takes two even spaces. The GE breakers need to straddle spaces. So the GE breakers you want to use won't even fit in the 2 spaces you cleared by removing the alien. They need to be offset by a half-space up or down, with other breakers moving around as needed, and half-width GE breakers deployed as needed.
Those require a special "magic bus stab" unique to GE, which adds a cruciform to the stab. Half-width breakers don't clip onto the stab, they clip onto the cruciform.
Those cruciforms stick out of the bus stab, and that Eaton breaker doesn't have a notch to clear them. It would not fit properly in a GE panel capable of taking double-stuffs.
Your panel DOES take the right breaker
Your panel label data clearly shows every space is listed for double-stuffs. You can use the GE 1” tall 240V breakers. So...
First the Eaton goes away. Byebye!
Now, the 240V breakers need to straddle the line between spaces. The old breaker was on even spaces, so you need to do something about that.
Move the "washer" breaker up 2 full spaces, so it is snug against the top of the gap.
Your panel is now ready for the two GE 1” breakers you asked about.
Remember the wiring is no longer inner/outer.