I'm looking for a form analytics tool that works on a page after the user has logged in. I came across some products that support heat map recording after login, but not form analytics. Is there any tools available on the market?
All of the analytics tools I have used work on any page, regardless of being logged in or not.
Even if your page is behind a firewall or not connected to the rest of the internet, you can still use tools like Matomo where you install them on your own server instead of needing to reach Google's servers.
If none of those are options, you can also obtain some data using server logs each time the form is submitted. This can be useful if you are mostly interested in error and success rates. You can even get a sense for how long people spend fixing errors by looking at the timestamps between events.