I'm aware that the teams are separate, however I imagine that key personnel and technologies can be/are transferred between programmes as required. No need to reinvent the wheel. Even the American MIC has movement of key engineers between competing for-profit companies.
Moreover, my main point was that in the 2020s there's now sufficient numbers of talented individuals to have fully staffed, separate teams work on next-gen programmes concurrently rather than sequentially. This is not a minor point, as Pete Hesgeth has been reported by Western watchers to oppose F/A-XX at the current time as he's concerned it will overstretch the American MIC and negatively impact the F-47 programme.
The FC-31 was a private venture by SAC before it officially became a military programme (with associated funding) to produce the J-35. So while the FC-31 tech demonstrator was made entirely by SAC's own talent pool, I suspect it was possible to requisition talent from the wider MIC (that largely exists under the state-owned AVIC banner) once it got picked for the J-35 programme starting sometime in 2021 (this date is based on rumours). Had the J-35 programme launched in 2012 when the J-20 programme was in full swing (first flight being merely a year before), that would suggest China's MIC at the time had sufficient quantity of engineering talent to develop both concurrently, but that clearly did not happen. Of course, this could have been down to China's different/smaller geopolitical aims at the time rather than MIC size, but it could have still played a factor.
We overtly know the Chinese MIC shares tech for 6th-gen because we saw UADF variants with J-XDS AMTs.