Mine is frameless, using L girders and cross members (which I call stringers). The legs are 1x4s, with countersunk screws and wood glue making a half-square. VERY stable legs. Same for the L gjrders. Crossmembers are screwed only so they can be moved if needed.
As you’re building yours framed, what will be on top? Plywood screwed to the frame? If so, glue would probably not be needed unless it’s luan or extremely thin. If extruded foam only, then I would use glue & screws functioning as clamps… which is what they are truth be told.
Pocket holes are really only for furniture where the hardware needs to be hidden from all viewing angles like cabinetry, drawers, dining tables etc. But whatever entertains you works I guess,
Your wife's opposition to gluing in the house is pretty silly... but don't tell her that in as many words. There's nothing toxic or harmful about wood glue, and you can't smell it unless you're right next to it. Unless she's objecting to your lack of good housekeeping and is afraid of the mess you'll make. Only you can say.
I agree, though that fancy woodworking and cabinet joinery techniques are way overkill. Butt joints are more than adequate. The only exception would be if your layout is in a real living space and needs to blend with the furniture.