The Theme Color Picker doesn’t work when...
In a document with artworks and images,

1. Select artworks and click the Recolor icon, then go to Advanced Option.
2. Enable [Open Advance Recolor Artwork dialog on launch]
3. Quit Illustrator
4. Open Illustrator
5. Select artworks
6. Click the Recolor icon in Control Panel
7. Disable [Open Advance Recolor Artwork dialog on launch]
8. Close the Recolor Windows
9. With the Artworks still selected
10. Click the Recolor icon in Control Panel again
11. Click the Color Theme Picker
12. Click on an image in the document

Results: Nothing!

To make it works again, we need to close the illustrator application and reopen it.

This is in 2021 and also 2022.