I have a EWR-PEK-RGN, BKK-PEK-EWR flight coming up in 2 wks.
Short layover in PEK on the outbound, longer on the inbound.
Has anyone transited through PEK recently? What is the situation like, and what kind of screening is done on both ends of the flight?

Ask the airline to reroute you so that you don't transit in PEK. The situation of the virus is not bad in Beijing but you will have tons of problems at the entry of Myanmar and the U.S.

If you're a US citizen or permanent resident, you'll be subject to a "self-quarantine" of up to 14 days on your return. As I read the announcement, if you're an alien with say a work or student visa, not a permanent resident, you won't be permitted back in the U.S. until 14 days have elapsed since you were in Mainland China. No exception for Canadians, either.

The other issue is whether or not those flights will be operating in two or three weeks, Look how quickly this is all moving.

The flight was on AirChina, I've canceled it already.
Have a CX booking on hold for the next 4 days. Not exactly sure I want to go through HKG either. So far Hong Kong has not been any more dangerous than other nearby places, but like you said this is moving very fast.

FWIW I went through HKG yesterday (as an exit point for China). Assuming that you don't have any options to fly more directly and assuming you still need to go to Myanmar and Thailand then HKG is a reasonable choice. Transit security had additional health screening but was efficient.

At the moment , would it be correct that a transit at the HKG airport between Australia and Finland would be acceptable

"At the moment" can change very quickly, including during your flight. It can also depend on your passport as well as the direction of travel.

Given current reactions, I wouldn't want to try this going TO Australia (although if you're an Aussie citizen and don't mind a two week vacation on Christmas Island or someplace similar.....) but going TO Finland with a Finnish or EU passport would seem "safer" especially if you're willing to risk being sent to quarantine, perhaps of the shelter in place at home sort.

BTW, can we assume that you mean a genuine transit without entering Hong Kong or leaving the airport, with a normal connecting time not exceeding a few hours? And will any luggage be checked through so that you don't need to go landside (and get your passport stamped) to retrieve and re-check a bag?