Do I actually need a USB4 or Thunderbolt SSD?

Only if your host supports it and you regularly move very large files. Reviewers from PCMag and r/UsbCHardware repeatedly note that 20Gbps and 40Gbps drives like the Samsung T9 and Corsair EX400U require specific host ports to hit rated speeds — on a typical 10Gbps USB-C port they perform similarly to cheaper USB 3.2 Gen 2 drives like the Samsung T7 or Lexar ES3.