Pimoroni's Tufty 2040 is a great RP2040 badge with an integrated TFT screen. 

• 2.4" colour IPS LCD display (320 x 240 pixels)
  • Driver IC: ST7789v
  • Connected via parallel
  • Dimmable backlight (adjustable via PWM)
• Powered by RP2040 (Dual Arm Cortex M0+ running at up to 133Mhz with 264kB of SRAM)
• 8MB of QSPI flash supporting XiP
• Phototransistor for light sensing
• Five front user buttons
• Power and boot buttons (the boot button can also be used as a user button)
• White LED
• USB-C connector for power and programming
• JST-PH connector for attaching a battery (input range 3V - 5.5V)
• High-precision voltage reference for battery level monitoring.
• Qw/ST (Qwiic/STEMMA QT) connector

I created a 3D printable badge which uses three layers to sandwich Tufty 2040. The three sections are held together using M2 18mm machine screws.

To power the badge, I used a 1000mAh LiPo battery which fits neatly inside the case. Note that Tufty 2040 has no charging circuit, so batteries / cells need to be charged externally.

The badge was printed using Overture Neon Green silk PLA on an Ender 2 Pro. 

I printed using the following settings

bed_temperature = 60 bottom_fill_pattern = monotonic top_fill_pattern = concentric bottom_solid_layers = 5 fan_speed = 100 0.16 quality 0.4 nozzle infill = 25% first_layer = 210 Celsius other_layers = 205 Celsius travel_speed = 100 perimeter_speed = 40 solid_infill_speed = 40 top_solid_infill_speed = 30 first_layer_speed = 20 infill_speed = 40