I do not think there's any standard way to externally make a browser navigate to an URL with POST method.
You better ask a new question with browser-related tags, asking if this is even possible. Only once you find out method to do this (and I doubt there is such a method), you can ask how to do it in Inno Setup.
Though do you really need the POST method? What for? Just modify your web application to allow GET.
Or is it is an 3rd party application, create your own page that accepts GET and forwards it to the 3rd party as POST.
If you need to hide the posted contents, what about:
- posting the data from the Inno Setup (HTTP POST request in Inno Setup Script)
- let the web application save the data somewhere (database, file)
- have the webpage return a token to the data (e.g. a database key, filename) in the POSTresponse.
- have Inno Setup open plain URL (GET) with the token (key) in the query string
- the web app looks up the data using the token (key) and present the results