Hello @Jean-Loup Orgitello ,
From reviewing the publicized list of resources that Azure supports for migration across subscriptions, SendGrid is not on the list.
Also found this open feature request for migration support for SendGrid. I would recommend upvoting this request to get more visibility to the Feature owners.
You may need to recreate the SendGrid service in the target subscription. Also not a bad idea to check in with SendGrid support for guidance.
Hope this helps and have a nice weekend.
cheers.