You should consider if it may be better to make it a bit more modular, even if it may cost a bit more.
For example, you could have a 50 cent microcontroller read the state of up to 16-32 buttons and send the data for up to 16-32 leds.
Each of these microcontrollers would use I2C or SPI or RS-485 or RS-232 (2 wires) and use another IO line as ENABLE (or give each a unique address through some jumpers on the board if you use i2c for example .. note i2c may have limit of up to 8 devices on one i2c bus, but in your case 8 devices x 32 buttons/led = 256 so you'd be fine even with i2c)
The microcontroller is fast enough that it can read the state of buttons tens of times a second and could even multiplex the detection of buttons to use less pins ... ex use 8 i/o pins to read the state of 16 buttons, or 12 IO pins to read state of 32 buttons (by reading 8 buttons at a time) ... and 2 outputs would be used for the led strip with 16-32 leds, and 2-3 wires for the hardware SPI/UART etc
ex a 60 cent ATTiny 406 with 18 IO pins would work just fine to control 32 buttons and a strip with 32 leds... and you don't need shift registers or whatever you thought of.
https://www.digikey.com/product-detail/en/microchip-technology/ATTINY406-MNR/ATTINY406-MNRCT-ND/8536649So then you're left with a controller that needs USB and Ethernet and way less pins... worse case scenario 2-3 pins for spi/uart + 1 enable pin for each "module", some ADC inputs for the sliders (but you could make a separate module for those if you want to)
It would allow you to use lower pin count microcontrollers... for example maybe something as simple as a PIC32MX may be enough :
https://www.digikey.com/product-detail/en/microchip-technology/PIC32MX664F128H-I-PT/PIC32MX664F128H-I-PT-ND/2601589