ModyBuchbinder already answered your question, but I have a couple more things to add to it.
You didn't directly call this out, but just wanted to say that if you already have an EGDB and then create a new table outside of Esri (like directly through SQL), then you will need to register that individual table with the DB (register with geodatabase tool). But, you do not need to re-register that DB connection with ArcGIS Enterprise. As ModyBuchbinder said, once you register the DB connection, all future tables will be included.
One other thing to note, which has got me a couple times, is that you are registering a specific version of the DB with the server. I've unknowingly been in another version of the EGDB that hasn't been registered with the server, and it asked me to register it when publishing. It wasn't until then I realized I was in a different version (of course this only applies if your data is versioned).