Secondly, your statement that this engine has much deeper throttling than YF-100 is not true.
Here is an extraction from a research paper from 2018. It says that YF-100 (1200kN LOX/Kerosene) is targeted down to 10%. It is much lower that this Methane engine 25%. More importantly, it has conducted many ignition tests.
Thirdly, I don't think the proposed rocket can share anything with CZ-5. LH2 and Methane are just too different in characteristics to share the same facilities, storage tanks and plumbings of the launch facility for CZ-5 won't work with Methane rocket. Just wait and see if SpaceX will ever reuse NASA's launch facility for SLS for their Starship.
Lastly, the replacement won't happen, at least not in the way that you suggested "common first stage". Just think about it, first stage is LO2/Methane, second stage is LO2/LH2, two different liquefied gases with far different temperatures, that is a nightmare. Think again, why does SpaceX use only Methane for Starship and SH? why does Falcon 9 only use LO2/Kerosene?
It can only be total replacement (all stages), new rockets. In that case Methane engine must have a tremendous advantage over the current Kerosene engines to warrant forgoing all the investment in CZ-7/8/5/9 and 921. It is akin to dumping your one year old Mercedes for a new EV because the EV saves you 10% of fuel cost.
That sounds fishy to say the least. The RD-191 for example can only throttle down to 27% not 10%.
I guess I did not make myself clear. The whole idea is to use a common LOX/Methane first stage engine across all the rockets instead of the combined LOX/Kerosene and LOX/Hydrogen engines currently used or contemplated. The LM-7/8 use the YF-100. The LM-5 uses the YF-100 and YF-77. The Long March 9 will use YF-130 engines. That is three engine types you need to manufacture and certify. This way you need a single engine type for the first stage of all those launchers. That is why I said "common first stage engine" not "common engine".
What SpaceX does with a common first and second stage is kind of beyond the point. SpaceX doesn't want to spend the engineering resources to develop a whole new rocket engine for the second stage which will be manufactured in small numbers and would require the use of different fuel. It is much harder to have ground handling facilities for hydrogen than methane. Just look at the boiling point of both. Methane has similar boiling temperature range to oxygen. Hydrogen is way, way lower. 20.28K for hydrogen. That is 20 degrees above absolute zero. Methane is 111.6K. Oxygen is 90.188K. The Chinese already have hydrogen production, ground handling, and the second stage engines already are in production. So the calculus isn't the same. LM-7 uses the same YF-75 engines on the LM-3A/B/C. The LM-5 uses the YF-75D, which is new, but it is capable of multiple restarts unlike their previous engine.
The move to a common first stage engine has nothing to do with saving fuel cost. It is all about driving down production costs through reducing the types of parts you manufacture. If you have those YF-130 engines only on a LM9 rocket which is launched like only once every couple of years how much do you think you will need to spend to maintain those production facilities, tools, and retain trained staff specialized in manufacturing those engines? The costs will be immense. It makes no sense. They need to rationalize the production chain in the future.
The 5m fairing production cost reductions because the diameter is same as LM-5 have nothing to do with sharing the tank design schematics. It has to do with sharing tools, production facilities, and logistics facilities to move things around. They have existing tooling dimensioned for that already.