No, they have not even that.
What they have is a Soviet made heavy aircraft cruiser, a domestic copy of the Soviet heavy aircraft cruiser, and one that is largely comparable to the Kitty Hawk class carriers the US launched in the 1960s (which is still undergoing sea trials).
The simple fact is, in a great many ways the "carriers" of the Japanese Navy are more formidable than that of China. Especially when considered what China will be flying off of them are domestic copies of a Soviet design from the 1970s. Meanwhile, Japan would use the F-35B, a significant advancement in almost every way.
Oh, and they do not have "two keels laid". In fact, they have no keels laid. The Type 001 is a single class of one ship. The Type 002 is also a single class of one ship. The Type 003 is a single class of one ship. The Type 004 is nowhere even close to starting building. They are planning on building 4 of those, but construction is not even expected to begin for another 5-7 years. They do not even have the power plants for the design finished, and that is not expected for another 3-4 years at a minimum.
Oh, and they are planning on using the J-35 fighter from that craft. As of this date they have not built a single one, not even a prototype. If you think they can crap out a 5th generation naval fighter overnight, I got some prime ocean front property in Arizona to sell you.
Especially when the J-31 is a navalized variant of the FC-31. That program has built exactly one prototype, which did test flights in 2012 and 2013. The very fact that the single prototype is all they have and it has done little in over a decade should scream how far behind that project is. To give an idea, the first prototypes of the F-35 were operational in 2001, and the first aircraft delivered to the military were in 2006. Five years from prototype to initial delivery. They are now at over 11 years with 0 aircraft delivered (or even close to delivery). China was relying on a lot of the money for that program to come from foreign nations, but everybody has given it a hard pass and they are on their own there.
You see, that is the problem when people try to simply make things up. Especially when they are things that are not hard to check.