The Vorosmarty ter and Basilica Markets are open and I visited today.
I was worried that the new management would not hold the same standards as the old management. I have been to markets in Germany, Slovakia and Romania and was disappointed by the extent of imported junk. In the past all vendors in Budapest had to submit there products months in advance for approval. I didn't know what the new management would do. Good news, everything was locally produced crafts, no imports.
The Basilica market did have some commercial sponsors and while that was a bit disappointing maybe the revenue pays for the the light shows and takes the financial burden off the local tradesmen and helps with their profitability. Wasn't terrible.
In general the markets are equivalent to the ones in the past that have received so many accolades and awards.
Crowds seem a bit lighter than the past which makes them very pleasant.
I only visited during the day. I will be here 3 more weeks so I saved the evening for another day. The difference between day and night is pretty stark. Good thing is sunset is about 5pm LOL.
All that being said, here are my snap shots. Watch for the evening photos (in a few days).
https://1drv.ms/u/s!Ai7Zk-szxfTJivgZNnTUG4HHktos8A?e=xISguv
The link is only good for a week,
The official site for the Basilica Market, but the main market on Vorosmarty ter is now run by the same group and 5 min walk away so I suspect the dates are the same: https://adventbazilika.hu/en
AND some more markets: https://community.ricksteves.com/travel-forum/trip-reports/more-markets-in-budapest-for-christmas-and-the-rest-of-the-year