You can use the wix-storage API to store values and share them with pages in the site.
First, you need to import the API:
import {session} from ‘wix-storage’;
On the page with the dropdown, you can save the returned value like this:
session.setItem(“key”, “value”);
To retrieve the value on another page:
let value = session.getItem(“key”);
Good luck,
Yisrael