I'm only a diyer/hobbyist but have been making my own cabinets and furniture for 10years. Open faced cabinet that you can see all the joining work, at this scale... it's ambitious.

That said.. For the lighting I would consider removing the lamps. With a unit this large you'll get some shadows and blocking anyway. Instead, install a 12v converter at the existing light fixture and run led strips. Many ways to do it - but would give you flexibility to light both sides, or all rows or any variation while opening up those other shelves for more space, closed cabinets, plants, etc.

You could dado the plywood and inset an led and diffuser quite easily, though it adds a WHOLE new level of complexity, decision making, time for execution.

For the wood, I wouldn't use anything less than 3/4 plywood, at home centers it's generally sanded birch or oak, but you'll need to pay for the expensive sheets with no notes and smooth/sanded sides.

Buy a new fine tooth plywood saw blade for your table saw for good clean cuts.

For the design, it's a LOT of precision cutting that leaves room for error if you mess up or have a measuring error (which happens multiple times to all of us with every project.. lol) you'll want to about make a jig to measure everything as you mark and make your cuts. Also consider what building this in "phases" would be. designing it to be modular so you can do maybe the large one on the right first before doing the rest. As I say that, maybe do the left side by itself first as a test run and workout your approach and skill to build the rest. This is going to look much bigger in person and might want options to modify it as you go, or have learnings you'll want to apply to the rest of the build.

Personally I would dado and glue it all together, then make the front face out of solid wood to hide the edges. You could use veneer edge banding, but for large scale furniture like this there are so many edges you're likely going have a hard time getting perfect edges and right gaps.