Any reason *not* to put electric oven on GFCI breaker?
Can't put a 15/20A recep on a 40A breaker
Any device in there would have, effectively, no circuit breaker protection at all.  Because the 40A breaker would be so far above likely practical short-out currents that it would not notice if the appliance burst into flame.  Rulewise:

210.21(b)(3) says on a 40A circuit, only 40A or 50A receps can be used.  (because NEMA never defined a standard for a 40A recep). It also says 15A receps can only be used on 15A and 20A circuits.

Next, 210.21(B)(2) says the recep loads can't exceed 80% of circuit ampacity.

Another rule says you can't have any receptacles at all on a circuit with hardwired loads making up more than 50% of breaker capacity.


Wait. Isn't the GFCI a circuit breaker too?
Nope. Actually the very opposite: 15A GFCIs are designed by the factory to safely allow 20 amps of passthrough - that's a UL requirement because 15A receps are allowed on 20A circuits.  So in reality, the GFCI has no idea what current is coming through it (only current difference) and will carry an overload right up until the point it bursts into flame.  GFCIs (and breakers for that matter) are not magic everything-fixers.
Your best bet is probably run a new kitchen circuit
One option is a multi-wire branch circuit. (MWBC).   That is a cable with 2 hots and a shared neutral.  I see at least 2 red wires in that panel, so it's possible you already have a kitchen MWBC, that would be neat because you could just convert it. But troublingly, it does not have handle-tied breakers.  On a GE panel, even that is not enough; any MWBC must use a 2-pole breaker!  (part of the reason for handle-ties is that forces the breakers onto opposite poles, an essential MWBC requirement; but that doesn't work in GE's half-width breaker design.  Only a 2-pole breaker is keyed/notched to only fit where it belongs.)
With the MWBC, you can put both 120V and 240V sockets on it.  One company even makes a combo 120/240V socket - one of each on a common-shaped duplex receptacle!
So if there isn't a kitchen MWBC, you could run one.  That will give you both additional 120V outlets and also 240V outlet(s).  This MWBC could replace your existing kitchen circuits if they are 20A breakered.
As far as GFCI, I don't see a sink nearby.  Unless the latest Code requires it, you may be able to dodge the GFCI requirement.  If you must go GFCI, it must be at the breaker. Definitely do the MWBC and definitely go 20A with multiple recep sockets, since you're sinking a lot of coin into that, so might as well get maximum bang for the buck.
That panel has serious issues
Somehow the panel's dead-front has disappeared.  I don't understand how that's possible, but what should not be possible is for curious fingers to touch any of the panel guts... or for that matter, for an arcing fire inside the panel to get out of the panel through gaping holes in the front cover.
I would talk to a GE dealer about getting the correct dead-front for that panel.  If that is not feasible, that panel is *grossly under-sized) for a house, so maybe it's time to replace it with a 40-space panel.