How to reliably detect HubSpot form "new form" submission event in Nextjs using embed script?

Thanks for the detailed answer!
Just to clarify, my main challenge is tracking the form submission in Google Tag Manager while using the embed script (not hbspt.forms.create).
I already have a new form and would prefer not to migrate or recreate it.
Is there any supported way to trigger GTM events with the embed script, or any recommended workaround?

Thanks again!