yes just like @lokki said that is essentially what you do with any element that is not fronplate-mount. try find bigger boards than the one you linked, so ideally you can squeeze 8 or all 16 of your buttons on one pcb. super cheap ones can be had from ebay "veroboard" is kinda the cheaprest but most wobbly material. for simple stuff make sure you get "stripboard" to make the wiring easier. what you posted kinda resembled the little plastic breadboards, where 5 pins are connected on each side. ideal for what you are doing just get a longer one.
this adafruit 3 pack is quite expensive but solid, durable material. you can google same thing in cheaper i am sure.
just beware of the cheap looking one-sided brown stuff, those are really loose and wobbly and will not be fun to work with. not recommending something like this:
same goes for screens: you wanna use the sdd1306 or whatever OLEDs that come pre-mounted on a little module/pcb. then you either mount this directly to the frontplate if it has mounting holes,. or you can also just stack this module on the same stripboard that holds your buttons.
if you want to avoid having any screws on the frontplate, you can either use spacers and mount it to the bottom enclosure (not advised) or use a 2-layer frontplate, lower one holds the mounting screws, upper one only has the cutout holes for the buttons/oled.
also, depending on the size of your project, sometimes it makes sense to outsource the UI stuff, ie. buttons, multiplexing, OLED, to a little teensy or arduino and just send data over midi. that way you keep all your precious axoloti recources available for audio. there's a lot of teensy that can easily do 16 digital i/o natively, for 20$. might be less effort than dealing with multiplexers.