Hmm, the only way I can think to do this is to add questions on Form #2, prefill them, hide them, and set the conditions based on those prefilled, hidden questions
For that to work you'd have a formula field that would create a link to Form #2 with the appropriate fields prefilled and hidden, and have an automation that would run when Form #1 was submitted thaht would send that link to the user.
This means there might be additional hoops for your users to jump through though, they'd have to wait for the automation to run and then open the link in their email, which might not be acceptable to you
I'm not too familiar with any other services that might do what you're looking for I'm afraid; hopefully someone else can suggest something in that vein
