I could be wrong but it appears this is not *just* a service panel, but is part of a larger machine, appearing to be a
Hayward E-Command pool controller. Note that this is a pool controller. I don't understand how it's possible for *everything* in this controller to not be GFCI. Is it fed from a GFCI in your main panel? (this is not your main panel).
The manual on this controller says, on page 6, which breakers you can use. This information is also on the panel label.
I don't know how those GFCI breakers came to be in this panel, but the manual appears to be calling out
Siemens QPF. What you actually have in there is
a Square D HOMeline.
For the twin breakers, it calls out a
Siemens QT. What you actually have in there is an Eaton BR, one each of the
CTL type and the
non-CTL type.
I don't know what's up with that. If the factory supplied the panel that way with three Square D GFCI breakers, maybe that version of their panel has Square D busing. Regardless, no way does a BR breaker belong in the same panel as Square D, and likely those are wrong too. Check the labeling of your panel. If that was done locally by jackasses, then don't invite them back. They just put $300 of the wrong breakers in your panel.
Anyway, no, those breakers are not GFCI breakers, and they need to be in order to be around a pool. Further, they are 20A breakers and I seem to recall you saying something about #14 wire - #14 isn't allowed on 20A.
The fat black wires appear to be bundled with the grounds, which tells me they are currently disused.
As far as not putting them on GFCI because that'd be inconvenient given the twins, if your insurance carrier knew about this, they'd cancel your insurance, and in fact, they may not cover you because of this known defect. There's a sad story every week about people dying around water features because of incompetent wiring. Maybe you can fit a GFCI recep in the 2-gang junction box there, so at least you have *something*.