How to connect my system to public sewage

Hi gang, asking for an advice. A house I recently bought is connected to public sewage and has its own septic tank. I'd very much like to fully utilize the public sewage option and abandon the tank. Currently only waste water (sinks/washing machines) is being drained by the public sewage connection. Here are some pictures (first two display the setup and the third one shows a possible solution:

I reckon the previous owner used a simple siphon to stop the smell from the public sewage.

https://preview.redd.it/4w45buhgznch1.jpg?width=2048&format=pjpg&auto=webp&s=344678a42c8c3b7f13119714449696a41953a8a7

So my idea is to simply connect the waste water pipe to the junction and then connect the bigger pipe to the public sewers (where should I use siphon if at all?).