Plans communicated from Google so far are for YouTube Music to function similarly to Google Podcasts, with a separate rss submission system. Until then, the podcast catalogue available on YouTube Music is populated from podcast channels on YouTube.
To get your podcast listed on YouTube Music, you will need to either submit your feed in Google Podcast Studio or create a YouTube Podcast Channel by following these steps. YouTube also have an rss ingestion functionality, which you can access by submitting your rss here. For help locating your rss feed, please refer to this guide.
If you already have a YouTube Podcast Channel and are not seeing your podcast on YouTube Music, you will need to reach out to Google Support.
Note: YouTube Music currently convert MP4 videos in your YouTube Podcast Channel into MP3 audio files for YouTube Music. Episodes are not currently pulling from your rss feed, so are cached on YouTube Music and unable to serve dynamic advertising or populate in your analytics.