web applications are a request / response. the browser requests (get) or submits (form post) and waits for the response html. when returned the browser pre-render the page.
on the server the request is processed by an action, and the view builds the html that will be returned to the browser (razor pages coming the action and view into one component). neither the action nor the view can change the browser until the html is returned. so while server side code to build the response html may be async, it still has no effect on browser until the response is returned.
to do what you want, you need to use client javascript to change the html after the submit and before the response is returned. typically you would attach to the form submit event, and make the desired html changes.
you can get more control, by having client script post the form data via ajax. In this case, the javascript needs to process the response data itself and update the html with server changes.