Solution 1 :

I’m not sure if that would be desired solution for you, but you could made template of document (current website) and inject the values from the form and compile with handlebars. Then use puppeteer to generate .pdf from that template.
It’s not the straight forward solution, but could work. I made something like that for my CV creator website. You may wish to check the code:

I hope its helpfull

Problem :

I would like the user to click a button which saves the current page as PDF, however I want it to include the values they have typed into the fields. I have searched Stack and many of the answers only allow me to save the original HTML form (sans values), or are deprecated.