I think a used condition Keychron (e.g. Lemokey P1 + M3 Mouse) could tighly fit your budget.

I would probably split the devices (2 receivers/usb), raise the budget a bit and get a wobkey crush 80 re, an Evoworks Evo 80 or if you prefer low profile, a lofree flow or logitech G515 tactile in used condition together with a cheap cable logitech G-series mouse