TFT_eSPI: Raspberry Pi Pico with Pico-ResTouch-LCD-3.5 not working

No, I don't have any Waveshare "Shift Register" displays.
I suggest that you adapt
C:\Users\ .. \Documents\Arduino\libraries\TFT_eSPI\User_Setups\Setup60_RP2040_ILI9341.h

e.g.

#define RPI_ILI9486_DRIVER // 20MHz maximum SPI

// For the Pico use these #define lines
#define TFT_MISO  12 //0
#define TFT_MOSI  11 //3
#define TFT_SCLK  10 //2
#define TFT_CS    9 //20  // Chip select control pin
#define TFT_DC    8 //18  // Data Command control pin
#define TFT_RST   15 //19  // Reset pin (could connect to Arduino RESET pin)
#define TFT_BL    13 // LED back-light

#define TOUCH_CS 16 //21     // Chip select pin (T_CS) of touch screen

#define SPI_FREQUENCY  20000000

Remember to rename your custom Setup file and select in User_select file

Untested. But it looks fairly straightforward.

David.