The words change but the self-serving policies do not. Remember what you studied about colonies? How about trade agreements and treaties. The Silk Road initiatives combine all of those elements to a degree but direct Chinese financing of infrastructure is the key element.
Your historical suggestions are incorrect. You're talking about a term while the subject is content.
The Chinese Belt and Road initiative is the core of their foreign policy. Mostly aimed at developing countries, they build infrastructure for them and fund it through loans the country ultimately can't pay back, at which point they take the asset under Chinese control.
Belt and Road Initiative - Wikipedia
When the US become the dominant world power it's approach to "empire" was different from any empire before. The US didn't physically take over any territory like the British did when they ruled the world. Instead the US helped enforce strict borders from the late 1940s with few exceptions and allowing for countries to break up into smaller countries. The US dominated the world economy and ran things that way.
China watched what the US did and adopted American ways into their plans for world domination. The Belt and Road is their primary way of doing it. China does not want to run the Russian government, they just want to own all the assets. They are patient and it's OK if it takes them 50 years.
This was posted today:
Opinion | How Vladimir Putin Lost Interest in the Present
It may be behind their paywall.
And this yesterday:
The Would-Be Czar's Dark Prophet | History News Network
They talk about how Putin has isolated himself to such a degree he only talks to two people now. One a modern day Rasputin and the other a Physicist obsessed with the past. Putin is stuck in a world of Russian Orthodox mysticism and obsessing about past grievances.
There has also been talk in the last 24 hours about how the Russians are planning to use chemical weapons. The Russian troll farms have been quiet in the initial phase of this war, but they are cranked up now spouting BS about how the Biden family owns 23,000 miles of tunnels under Ukraine where they are producing chemical and biological weapons. And predictably one wing of US media is running with it.
So we have someone with complete control over Russia with no official checks on his power who is only listening to a couple of loons and his propaganda network is cranking up the usual suspects in the west to trumpet BS on his behalf so he can justifying the extermination of the Ukrainian people with chemical weapons, nukes, or both.
I think this may be the closest the world has come to nuclear war since at least the Cuban Missile Crisis and quiet possibly ever. I can't see any way out of this that can be orchestrated outside of Russia. If someone took initiative and welded the door to Putin's bunker shut before turning off the power, the world could stand down. It might take a while to sort out the war and Russian internal politics might get very messy for a while, but at least we would see deescalation from nuclear war.
There is no active role (no fly zones, putting troops in Ukraine, or even transferring aircraft) that anybody outside of Ukraine could do that doesn't carry an extremely high risk of this spinning up to a full nuclear exchange fairly quickly. That's the facts. You can't impose a no fly zone on someone who can violate it catastrophically.
I feel the frustration, but picking it up from others and personally. One of the toughest things in the world is caring about a situation and watch it become a horrible mess and knowing there is absolutely nothing you can do to stop it. I've dealt with it many times on a personal scale when someone I care about does something stupid and self destructive and I've had to sit by in larger scale things that were going wrong and I was unable to do much about it. We've all lived through several of these the last few years.
I'm hoping somehow we will not see chemical, biological, or nuclear weapons used anything, especially not in this war. But I'm getting less optimistic. In a straight up conventional weapons fight, Ukraine will win and probably pretty decisively in the next few weeks. It may take longer to get the last Russian off Ukrainian territory, but conventionally the Russians will be unable to do much offensively in a few weeks.
If the Putin decides to make Ukrainians extinct, I don't think the world reaction will be very pleasant for Russia, but it won't help all those killed in Ukraine.
