there is no bridge wing needed. this is just like what the lafayette class has, indeed, and serves as bridge wing perfectly, although it is part of the bridge itself. it is simply an plated over space on the same position as the dutch LCF and SIGMA ships have, for example, and is quite similar to the bridge wing of the nansen too, although that one is glassed more.
maybe you don't know it, bezo, but ship stealth is more often refered to as 'keeping missiles from hitting us' then really 'hiding where the ship is' and thus, giving that task to bays and inlets, is useless in an modern combat environment, even in the philipines.
I would actually NOT integrate the CIWS with the structure, if the ship operates in confined (littoral) waters, the CIWS should be able to have an as big as possible field of fire and an low weight (non-stealth) as possible construction, for fast operation.
the arnament mix looks good, there are only 2 things I would think too much or too expensive for the philippines keeping in mind their current plans:
-the SLQ-32
-the automated gunmounts amidships.
I would also consider a bit of a tonedown on the VLS, to an Mk 48 or an 8 cell Mk 41 module. 64 ESSM on a ship like this seems a bit like overkill to me, but this of course depends on how many reload abilities there are and the number you have available.
another point you would have to check, is if this radar fit works: IIRC, CEAFAR works with an separate air search radar, like SPS-49. I might be wrong on that, but I would think you get at the very least an search range penalty if you leave it out.
FYI, the Philippine Navy is actually planning to buy the same kind of automatic gun mount installed on this ship. Read
this article on timawa.net. And the Israeli Sa'ar 5 corvettes have as 64-cell VLS.
Update: Added lightweight torpedo. Mk. 32 torpedo tubes are hidden behind the small shutter.