That’s the SMTP envelope-from, not the From header. The From header is not used for bounces.
i.e. ① not ②:
To pass DMARC, either the SPF (which validates the envelope-from in combination with the sending IP) or DKIM (which validates the From and checksums fields of the message) have to align.
It sounds like the whole point of this exercise is to have a “pretty” reply-to address, that users reply to?
You want something like this?
envelope-from: outgoing+12309847801923840923502389423@yyy.com
…
From: notifications@yyy.com
To: user@contoso.com
Reply-to: my_sweet_forum+12309847801923840923502389423@gmail.com
You must have that envelope-from like so, or bounces will not work.