After putting the tinySA in DFU mode, you need to use the small icon with two up-arrows to open the firmware update window.
Then see if the DFU device shows up in the drop-down list in that window.
If it does not show up, make sure your cable is really a data cable, and then make sure you have the correct driver installed.
For driver instructions, see the instructions file in this folder:
(yes, it is for nanoVNA, but tinySA uses the same driver for tinySA-app as is used in nanovna-app).
