Resolved – configuration issue on my side.
Update : It seems the URL is well updated with the transaction ID and the token.
If I open it with the same format than a web Payin without the template option I can reach the the webpayment page URL.
(base: https://api.sandbox.mangopay.com/Content/PaylineTemplateWidget?rp=57c5e8395493496f99e2199f1457b2bf&….)
So I believe this issue is only that the Woocommerce checkout default page isn’t by default understanding the new URL.
Still working on it, but if you have any direct solution I’m listening 😉