The editor shows at most 16 foreground and 16 background colors at a time.
However, I discovered that as of the Windows GUI version of TSE Pro v4.2 there is no such limit in its programming language, provided the screen is not refreshed.
That opens up possibilities.
One such possibilty is a color picker, where a TSE screen shows thousands of colors, and lets you pick one by clicking it.
Download page:
https://ecarlo.nl/tse/index.html#ColorPicker