Sorry, but with your sample code, dropdown is not even populated.
Please help us help you. At least try to make select render with options in UXP. Currently you’re asking how to fix something, but the issue is not even there. It seems like you’re assuming there’s going to be an issue and already asking for a solution.
Here are the docs on how select (aka dropdown, aka picker) works in UXP. Here’s how I use it.
From the code pieces provided in your last post, I can assume where the issue is, but you won’t be able to test it until you have picker working. You’re changing only value of the option, and you need to change both value and text