Auth Email with SMTP provider: Using SendGrid Dynamic Template

Howdy! We are migrating to Supabase from our internal Auth system, built-in into our Backend stack (Node.js + Express.js + Loopback.js v3). I have been able to properly setup SendGrid as a third-party SMTP provider, and it works: if I request a password reset or I invite a new user, I correctly receive the transactional email from my SendGrid custom domain. Only problem: we use Dynamic Templates on SendGrid, created with its editor, and we'd like to keep using them without copying and pasting the SG template HTML into Supabase. Using SG API, it is possible to specify which template to use, and which parameters to pass through (more info here: Is it possible to add in Supabase Auth -> SMTP settings, or in the Email Templates settings, the chance to set up templates id for each Auth transactional email? I already looked over a possible workaround: using Edge Functions + Auth Hooks. It works, but for some reason I'm not able to receive the correct parameters …