First of all, filetypes.common is syntactically correct, because it reflects my other changes I made there (for instance, making the cursor wider).
But I found that restarting Geany helped, and I can now see the changes.
My guess is that Geany does not monitor the theme file and one needs to reload it somehow. Indeed I could verify this:
Now that I can see that the settings basically do take effect, I now changed the value again from the one I used for debugging (plain red) to a more suitable light yellow. Again after I saved the theme file, the old (red) value still was persistent, but once I switch in Geany to a different theme and back to _tinge_, I can see that the changes work.