It is absolutely normal and to be expected that China would be working on a single engined stealth fighter. Something needs to replace all those J10s eventually. And those replacements won't be happening in 5-10 years time, when stealth would still be something a bit expensive, but in 2030s, when stealth planes will be the norm for every half-decent (not cash strapped) air force around the world.
So, if preliminary work has started, then some digital prototypes may appear in early 2020s. And a flying prototype may appear by mid decade. Entry into service may be achieved by 2033 or so, with steady production and gradual replacement of J10 until 2050s.
I don't believe it'll be a STOVL plane, though. And going for F-35 kind of unification seems less than prudent. So *IF* there's going to be a manned STOVL plane from China (which in itself seems unnecessary to me) i'd put my money on a separate project, a different design which then may share some subsystems and perhaps even the engine core.
As for the engine itself, that's a no brainer. Some future WS-15 variant for the single seater seems like a given.