Is there a flush circuit breaker box cover?
Holy smokes, no! Panel covers are not junction box covers!
The panel cover MUST be flush with the panel.  There is no choice nor option to that.
It doesn't work at all to have the cover be out of position. The cover being flush is essential to the  breakers not falling out!! That would be clear if you understood how breakers attach.

Use the surface mount version of the cover for that panel.
Which manufacturers usually are willing to sell separately.
The surface-mount version, instead of having a big flange to cover up the drywall edge, simply is bent 90 degrees at the edge. It adds maybe a 1/16&quot; margin to the box size.  You will still need to plane or saw down the 2x4's a little bit, but it should be feasible.
Honestly, I'd cut back the drywall and 2x4 a lot more.
The reason is, as usual, no thought was given to finish treatments for the inside edge of this frame.  So I'd actually remove about 1-1/4&quot; from all four sides, so there's room to frame it in stainable wood 1-by's. And I'd create that box of 1-x's on the bench, built so the inside is 1/4&quot; larger than the panel cover.... (and this would work with the original panel cover too).
Then having cut back the 2x4 material and drywall, I'd reinstall the panel cover, then shim the frame/lining so that it is dead nuts square on the panel cover with 1/8&quot; margin on every side.   Screw it down.  Then stain it with a tasteful stain. Finally I'd fit a cosmetic fringe around the opening to hide the ugly gap between box and drywall.
For bonus points, you could simply put a tasteful cabinet cover over the whole shebang, then you wouldn't need all that trim wood.