You need to use the TWCore <$select> widget, not the HTML <select> element. Otherwise, your selection will not be stored anywhere.
You must also specify a target tiddler (or at least a target fieldname); e.g. <$select tiddler="MySelection"> or <$select field="myselection">. Otherwise, the widget will default to setting the text field of the current tiddler, which would immediately overwrite your code as soon as you make a selection!
You may also want to specify a default value to use when the target tiddler or field doesn’t exist.
This was just a theoretical question, I ran into this while experimenting with filters. Of no immediate practical consequence, but thank you so much for that tip!
Thank you @EricShulman , I need to play with all this. Trying to grok TW concepts and this definitely helps. This is a great start for me – spent a bunch of time googling last night and couldn’t find a definitive pattern. Thank you so much.