Based on a comment on this answer:
So to help clarify, in that cavity in the pictures, if I stick my finger inside you can feel a hole which is the overflow dumping into this opening. It's clogged with muck (that's just something I need to clean) but indeed I'm convinced this was a hard plastic seal to protect what is underneath: OSB/fiberboard. It's not a solid piece of porcelain and I can see this on top for the faucet opening in the holes drilled. Therefore due to that hard plastic sealant/coating/etc in all those pictures I'm 99.9999% sure it part of the sink & not replaceable. I will need to fix up the damage & add sealant
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atconway Emphasis added
If there's some sort of particle/fiber/chip board in this sink as part of its construction, then the only thing I could recommend in good conscience is that you contact the vendor of the sink and get the proper repair instructions and parts directly from them.
Any sort of wood-based product in the sink bowl itself is exceedingly unusual, especially the types you mentioned, since they are very susceptible to water damage.
Based on the pics, it almost appears that this is part of the drain overflow mechanism, however, the wider shots don't show any sort of channel to bring water here from the overflow drain somewhere near the rim of the bowl.
The part in the red circle (below) seems to be somewhat bodged on (based on what looks like a large amount of silicone(?) sealant (in the green circle).

Click to embiggen
If this is, in fact, part of the overflow, then you may need to contact the sink's mfgr. (one pic shows part of a label that probably has the mfgr. name on it) to find out what kind of drain kit is required for this. It appears to me that you'd need to seal the drain on the inside of the bottom opening to catch the water from the overflow. Using a standard drain (if you could somehow wiggle it between the two layers) would leave the more visible opening in the sink exposed and without a drain, and that would be very odd looking, at best.
If this isn't part of the overflow drain, but just "something weird", pictures of the original drain would help, I wouldn't think you'd need anything special to seal this. Just get the main bowl opening cleaned up back to bare porcelain then install your new drain according to the drain manufacturer instructions. The tail piece of the new drain should be more than long enough to go through the 2 layers of porcelain here and connect with the DWV plumbing below.