N.T.'s answer is sufficient, I will just add this. You are asking a good question. The whole background is basically this: God gave us 613 general commandments, and then an Oral Torah to explain them, as well as a general charge to the Rabbis to work out more details, add guards and fences around them, and innovate time sensitive decrees according to the rules and methods laid out etc. There are also customs.
All of the above is what you mean when you say you are looking for something more than just the 613 commandments, and quite right. Until Maimonedes, there was never a comprehensive book that just collects and categorises it all neatly and without extraneous discussion. Since then, we have several, arguably the most important is the Shulchan Aruch.
The Shulchan Aruch is very long, and itself has dozens of commentaries. Even though it is very long, it doesn't cover everything! Not just laws that are no longer possible to practice (such as laws pertaining to when the Temple is standing) are omitted either. Trying to condense everything in the Oral Tradition is an endless endeavour and the author did have to draw some lines. Gaps are filled by later works and commentaries (a big one is Mishna Berura), and there have been further attempts to condense things even more concisely and practically, as N.T. has mentioned.
A comprehensive and complete work on this is the Mishneh Torah by Maimonedes. It is available online on Sefaria in English and claims to cover the entire Oral Tradition. It seems more in line for what you are looking for, if I am understanding the question correctly. Contained in these laws are what gentiles are and are not allowed to learn, so anyone reading this should bare that in mind.