Definately go Raspberry Pi, it's a linux PC with great hardware and GPIO capability, as well as all the connectivity you could want (SD, BT, etc). The core of this challenge is the keyboard, so depending on whether you are willing to build your own or need to find a kit, etc. will determine what is needed for connections. If it is something pre-made, or at least a pre-designed kit, you might get something that is USB plug&play or Bluetooth. Otherwise you are talking about building and wiring each of the buttons individually, and then collecting those signals via some version of a "multiplexer" circuit.
most direct route would be to get the Keyboard premade with all the buttons and backlights ready (like the link below), and run it and your display with a Raspberry pi hidden in whatever 3-d printed case you choose.
https://www.amazon.com/Typewriter-7KEYS-Mechanical-Bluetooth-Connection/dp/B092HVXVM4
Retro Typewriter Keyboard, 7KEYS Electric Typewriter Vintage with Upgraded Mechanical Bluetooth 5.0, Multi Devices Connection Classical Wooden, Punk Round Keys for Desktop PC/Laptop Mac/Phone https://www.amazon.com/dp/B092HVXVM4/ref=cm_sw_r_apan_glt_fabc_7VT68R51MP998A0VB5DZ?_encoding=UTF8&psc=1
Retro Typewriter Keyboard, 7KEYS Electric Typewriter Vintage with Upgraded Mechanical Bluetooth 5.0, Multi Devices Connection Classical Wooden, Punk Round Keys for Desktop PC/Laptop Mac/Phone https://www.amazon.com/dp/B092HVXVM4/ref=cm_sw_r_apan_glt_fabc_7VT68R51MP998A0VB5DZ?_encoding=UTF8&psc=1
Retro Typewriter Keyboard, 7KEYS Electric Typewriter Vintage with Upgraded Mechanical Bluetooth 5.0, Multi Devices Connection Classical Wooden, Punk Round Keys for Desktop PC/Laptop Mac/Phone https://www.amazon.com/dp/B092HVXVM4/ref=cm_sw_r_apan_glt_fabc_7VT68R51MP998A0VB5DZ?_encoding=UTF8&psc=1
Retro Typewriter Keyboard, 7KEYS Electric Typewriter Vintage with Upgraded Mechanical Bluetooth 5.0, Multi Devices Connection Classical Wooden, Punk Round Keys for Desktop PC/Laptop Mac/Phone https://www.amazon.com/dp/B092HVXVM4/ref=cm_sw_r_apan_glt_fabc_7VT68R51MP998A0VB5DZ?_encoding=UTF8&psc=1
This is an actual keyboard on Amazon (not an affiliate link) https://www.amazon.com/dp/B092HVXVM4/ref=cm_sw_r_apan_glt_fabc_DTDYW1ZJDEXKNJEAGNC6