Yes, I should have used the phrase "landing on and/or taking off from" instead of "operating from". My bad.
Regarding the rumor - The rumor was basically from a comment which has been quote-posted on Weibo:
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This guy claimed that Shandong will be the 1st one to have J-35 landing on and/or taking off from her flight deck, which I will translate-paraphrase here:
However, until there are clear evidences that the Shandong was commissioned in late-2019 with the capability to operate J-35s from the get-go, and/or (semi-)official indications that the J-35 will be operating from Shandong in the future - I'd like to keep the observation open for the time being.
This similarly applies to one suggested possibility that one of the upgrades done to Liaoning is the installation of facilities and infrastructure required for the future operation of the J-35s from Liaoning during her the recent-&-ongoing MLU at Dalian.
Hence, my original statement of "it might be a good idea to keep a lookout on the STOBAR CVs".
Of course, given the reputation of this guy in particular, again, caution is advised.
(Side note: Regarding the KJ-600 - While an E-2C is said to have performed unassisted ski-jump takeoff tests some years ago at a land-based facility, no such thing has been done with the KJ-600 as far as we know. Hence, my intention to keep the KJ-600 out of the discussion.)