According to the YouTube Terms of Use, the service is provided by YouTube LLC, USA. Thus, it is already subject to the consent requirement due to the transfer of data to an insecure third country pursuant to Article 44 of the GDPR (cf. ECJ ruling on the Privacy Shield and the Cloud Act).
Solution approach:
Instead of the YOUTUBE code, place a thumbnail on your own website and link it to the YOUTUBE video. This way, the notification problem is transferred to the operator of YOUTUBE.