I had to skip a lot of threads due to dinner but I wanted to say there really isn't a legal category for "suspect." These are words the media uses to describe ongoing investigations. I'll briefly describe the legal statuses we pay attention to as they trigger different rights and protections. I'm just going to use plain English so please do not reply to me linking to some law dictionary saying I'm being too casual because the point of my post is to explain the layout so everyone who reads it can understand what's happening.
If someone has information related to a crime, they can be a witness. A witness has relevant information either that a crime has occurred or relevant to a police investigation.
Once police have probable cause that a person has committed a crime, they can go to a judge and get an arrest warrant to detain them. So there can be a warrant out for someone's arrest. LE can request to seal the warrant so it isn't public as to not tip off the subject. Right now, it is totally possible that LE has a sealed arrest warrant for Brian's arrest. If that was the case, they would NOT announce it. They need to locate him in order to arrest him so what they call him before the physical arrest is really immaterial.
Once a person is located, LE can "detain" them. Detain means you can't leave. If your liberty is restricted, you are detained. Once you are detained, certain protections kick in. You have the right to remain silent. You have to be read your Miranda rights. There are Supreme Court cases that have litigated your Constitutional rights and when they apply (detained, arrested, charged, convicted).
Once you are served with an arrest warrant, you are under arrest and you are detained by the police. All the same protections as being detained without an arrest warrant apply.
After a certain amount of time detained, you have to be charged with a crime. That officially makes you a criminal defendant. Depending on the state, you can be charged by the DA or there can be a grand jury that indicts you. Once you are charged and you are a criminal defendant, other protections apply - like your right to a speedy trial.
So LE wants to make sure they have their ducks in a row before they make these official steps. They can have an internal "suspect" early on but due to not wanting to tip off that person they never announce that they have a "suspect." Othertimes they can announce right away that someone is a suspect or a person of interest because they believe it will put pressure on the person or witnesses to come forward.
LE has information officers because dealing with the media has become a big part of policing these days. But LE has no obligation to announce anything to the media. So I would not focus too much on what LE is saying right now in terms of is he a suspect, is he a POI, do they have evidence.
LE had enough evidence to get a search warrant for his home after his parents refused (so no consent). A judge reviewed the evidence they had and granted it. So I definitely would not conclude they do not have enough evidence to arrest him - they need to find him before they arrest him!