I mean, yes, the sources you cited are generally right. I'm speaking from experience here, so I don't have data, but I believe my experience to be generally reliable. For long distances, there are a lot (I mean a LOT) of discounts on flights, but hardly any for the railways.
I picked a random date and a random pair of large cities that are quite far away from each other, say Changsha and Beijing, June 18th. The cheapest flight is 500 CNY and cheapest bullet train is 649 CNY, so indeed the flight is cheaper.
In fact, I originally chose Guangzhou to Beijing, but due to the current epidemic situation in Guangzhou, the flight prices were negatively influenced (the flights are as cheap as 300ish yuan, due to very low demand perhaps).
But for mid-ranged trips, e.g. Shanghai to Beijing, the cheapest bullet train is 498 yuan and the cheapest flight is 568 yuan, so it does not really make a huge difference here. However, the cheap flights fly into Daxing, which is really far from the city center.
Time wise, even if one add the time required to travel to/from the airport, and the extra time required to board a plane, the airplane is still almost always faster. HSR stations are often also far from the city center, and there's also a line for security, so there isn't much of a difference here.
But often, for medium distances, the best deal is (at least used to be) the sleeper train. Sleeper trains are quite fast (the Z and T trains can run up to 160km/h), and since they run at night, you don't "waste time". I used to be a frequent passenger on the T32 sleeper train, travelling from Nanjing to Beijing W. It's dirt cheap and there's a kitchen on board for late-night cravings.
Unfortunately, like many other Z/T trains, T32 has been replaced D32, operated using CRH trains. The D sleepers are more comfortable but more expensive, making them less competitive than their Z/T counterparts (but you still save lodging!).