How to get all posts assigned to a taxonomy term only?

Well, you can do it in many ways. You can introduce a form with a drop down input for the terms and pass it to a function through POST or GET method and the query the posts associated with the terms, then show them. Fro capturing the send data you can use admin_post_{$action}. Read thoroughly the documentation and do some search, you’ll get necessary information to make this thing work.

You can use AJAX to make this thing more robust. For AJAXifing the system you can have a look at those below links-

  1. https://codex.wordpress.org/AJAX_in_Plugins
  2. https://codex.wordpress.org/Plugin_API/Action_Reference/wp_ajax_(action)
  3. https://codex.wordpress.org/Plugin_API/Action_Reference/wp_ajax_nopriv_(action)

From your question this is the only thing right now I can suggest.

Hope those helps.