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Have they made it so impossible dates are impossible, I wonder?
Doesn't seem like it. Using the interactive board on the website I was able to produce a solution that only revealed numbers.
Creator here. No, you can arrange the puzzle pieces to make dates that don't exist, like Monday February 31. Actually there may be "impossible" dates, because I didn't check for them, but I guess all combinations of days of the week, day of the month and month are possible. And also many non-dates, like 1, 2, 3. But good point: alle possible dates have at least 1 solution. Disclaimer: I sell these puzzles for a little more than the raw material.
I have the "A Puzzle A Day" https://www.dragonfjord.com/product/a-puzzle-a-day/ since a few years and I have thoroughly enjoyed it.

All dates are possible and most (all?) have multiple solutions.

Creator here. That puzzle started my search into this type of puzzle. But in the end my puzzle is harder, because it also contains the day of the week and has the most "irregular" puzzle pieces possible.
Those particular rhombuses are typically known as "squares"
Creator here. I know, I know, the "rhombuses" are just rotated "squares", but I already had a calendar puzzle "Square", so that's why.
Nice, but it's only available in English sadly, there's a link that says "see kalenderpuzzel "Ruit" for the Dutch version" (I'd prefer French but Dutch would do as well) but that page says "De maanden en dagen van de week zijn in het Engels".

The "square" one is in Dutch but sold out and the Rotterdam one in English only.

But I like that idea, apparently it's not the first puzzle of this kind but I didn't know about them.

Creator here. If there is enough demand I can make a French version. Ordering a new batch of lasercut wood cost me $20, so I have a minimum batch size of 20.
Seems pretty hard! Even the easy example.
Creator here. I sometimes advise people not to focus on today's date, but a date in the following week. Then you have more time to find a solution!
Ooh, nice white elephant gift idea for work. I never know what to give.