What I notice is there’s all kinds of options out there, so many that it’s hard to figure out what the right thing to do is. When I’m looking for an answer, I try to see what the best ones have to say. It’s all over the place even with them. One of the best shooters I like to listen to is named Eric Cortina. He does an abrasive cleaning to his barrel, but not regularly. He also says there’s no need to break in a barrel and I’ve heard other smart ones say that it is. I know people that clean after each session and I don’t have a problem with that. A lot of those will go months without shooting, so there’s not a lot of volume. I keep track of how much shooting I’m doing to how much cleaning I do. That usually means about 150 rounds or 3 plastic cases of cartridges and I’m cleaning. For me that is about once a month for the lightweights, Varminters to 06, and about once a year for the magnums. When I clean, I make sure I’m not too aggressive. Never use a brass brush and instead use a nylon. Rimfires and pistols can get real dirty so it’s not unusual for me to clean after every session. For rimfire, that’s about 100 rounds per trip, pistols 2-3 times a year.
For a new barrel, I will clean like you mentioned. After each 5 shot group or sooner, at least in the beginning for the first 40 or 50 rounds. I don’t know if it works, but at least it’s over quick. Just make sure you’re not getting the barrel too hot and it should be fine.