Unmarried with vietnamese child, what are my visa or TRC/PRC options?

I just went through the process of acquiring a vietnamese birth certificate with my name on it.

I built a house for the mother, which she is the land and property owner, but we are unmarried.

Right now I'm using a regular tourist 3 month visa. I'm looking to understand my options for getting a more lengthy visa or ideally a TRC to avoid hassles when leaving and entering the country, and to stay in Vietnam for a more extended period of time.

I've read that there is now a TRC available for parents of Vietnamese citizens, which I am. But it seemed like this may be difficult to aquire if I'm not married to the mother. Can anyone help me understand what my options are? Or tell me some resources available/government offices located in Hanoi that deal with this type of issue.

I reside in Hanoi at the moment in order to register a birth abroad with the US Consulate, but my child and mother live in Quang Tri. I registered with the local police department in Quang Tri when was getting the birth certificate, stating that I was living in the house of my child's mother. It was a temporary registration, I told them 3 months (the length of my visa) which they were a little uneasy about to begin, telling me that was a long period of time to "temporarily" stay. And if I were living there any longer than the 3 months, I would need to file a different type of paperwork, which I assumed by perhaps a permanent registry. If I were to apply for a TRC being the father of a Vietnamese citizen would this be done in a major city such as Hanoi or back in Quang Tri because that's where my child lives and where I can register with the local police office?

The local police office didn't give me any type of official documents or papers showing that I had registered. And I wasn't added into the mother's blue household booklet. I've read that it is illegal to live with someone when you're unmarried, but this was a post from ~2014, is this still the case?

Any advice or information would be a big help, thanks so much.