It's a wild guess, but a setup like this can be used to implement the 15bpp + 256 color palette graphics mode, that is not supported by either the SC11486 or the KDA0476 chip. These DACs can be blanked on a per-pixel basis, so there could be logic on that card that looks at the top bit in 15bpp modes (which is not used for color determination), and blank the Hi-Color DAC if this bit is set, but blank the 256-color DAC if this bit is clear. Using two DAC chips to implement that mode is a very crude solution, though, because there are DAC chips that natively support that mode. Possibly Sigma got these "older" DAC chips at a cheap rate and they tried to sell on the 15bpp+256 feature without having to buy a more modern DAC chip.

Now I'm wondering what software would be necessary to use such a feature...
Can generic ET4000 drivers do that?
Or was there something specific to Sigma Designs?

The 32K+256 color mode never was common in PC system, although it was supported in some graphics abstraction layers. I'm actually unsure whether then Windows 3.1 graphics driver model and/or X11R6 provides such a mix (IIRC it's possible that an X server exposes different "visuals" with different color properties, and lets applications choose on a per-window basis which visual is used with that window). I know for sure that the official Tseng BIOS (which is specified in the ET4000 data sheets) does not expose these kind of modes, so any generic ET4000 graphics driver will not be good enough. You need a driver that knows (a) that this mode is supported and (b) how to activate the mode on this card. Step (b) might either be a vendor proprietary BIOS call or some direct port access to the graphics card.

By the way, that card seems to be a "Sigma Designs VGA Legend II", see https://wiki.preterhuman.net/Sigma_VGA_LEGEND_II . I read quote of a review from a contemporary PC magazine that praised the precessor of that card for their easy to use and comprehensive driver disk, so I might be able to find vendor-specific drivers for this card, too.

So it would allow to run a GUI system in HiColor, with a windowed app using palette effects... fascinating, though very niche.