I built apps like these on GOV.UK over 10 years ago for the Ministry of Justice. We built our own form wizard library that let us validate long forms in steps and break them out into multiple pages because Ruby on Rails didn't support doing that out of the box. It was a very important principle back then that everyone should be able to make use of these digital services regardless of whatever users were using to access them.
I've always liked basic HTML pages where one can upload a document without having to restart the entire application. That's a great practice you have there with general forms. With each session ID, it can cross reference a page in a multi page application with that session ID, so that the user can maybe type it in if necessary, but it should be able to determine that with enough information, like IP address, upload date, browser, OS and so on. But the most accurate session would be within the browser so that the cookies for a single application aren't mixed up with another applicant, like a relative, who might be using the Playstation Portable.
I am actually impressed by the gov.uk websites. Its minimal and just about right for its purpose.
May I ask what tech is used for mobile apps? I am guessing not a full mobile app but it uses webview.