How do I create a clickable map where clicking on a specific part of the map takes you to a webpage using QGIS?

If you are using a CMS like WIX, there are a lot of javascript libraries that you can use to implement your map fast and easily. For example, amchart has a map component that can be implement using js and you can add click and hover event to the map. If you are not familiar with this, just take a look at its demos.

If you need something more powerful, you can use leaflet to display a map and add some different layers on a based map like open street map outdoor layer which is good for your application. This is an example of leaflet.

With qgis2web export leaflet you can create a nice map. But I think, a directly link is not possible. However you need for all regions informations, for example the name of a region. And in addition you can insert hyperlinks to other internet pages. This ist not a problem, because you can insert html within the table. For example: If you insert https://www.berlin.de you can see the clickable link "berlin.de" within the popup of the region/polygon. Now it open a new tab in the browser.