The choice list can be edited after the fact, new items will be in the dropdown menu next time it is opened. BasePopupField.choices.set is virtual public, has been for a while, but there were some other changes in the code over time. What version are you using?
When testing here, I am able to see the option added. Does this work on your end? (when you create+ add a choice straight after)
It is just a dummy test window where I create a dropdown with a few choices, and then add the “Test 5” option. (You can see the relevant code in the background). The Test 5 option is on the list and not disabled.
You will need to share more (the template, all relevant uxml, uss, c#) so that we could investigate this. You could also fill a bug with your project and clear steps to reproduce the issue for someone else at unity to investigate this, but it usually takes longer to get an answer than the forum.