Apple watch SE does not always recognize magnetic charger

If you are plugging it into a laptop to charge your watch with the USB-C cable, sometimes the laptop may be trying to read what kind of device is plugged into it and may not be sending out the charge. USB-C is two way, just plugging in a device doesn’t start the charge power to travel through the cable. This is because if you have two devices trying to supply power it can cause a problem with power trying to travel out of both ports at the same time, the devices need to talk to each other to tell which one should supply the power. It’s not really a problem, it’s more of a communication thing and it happens. I would suggest plugging the watch into a power brick or some other sort of power station. You will probably see that this issue will go away or not happen as often. A USB-A watch charger could also be plugged into your Windows laptop and this will correct this issue as well. USB-A works differently and automatically supplies power, this is why you don’t see very many USB-A to USB-A power cords because both of them would automatically try to supply power causing damage to one another. If you plug in a USB-A watch charger then you’ll automatically be supplying power to the watch without using that two way communication and you’ll not get that error. Either of these methods you should see correct your issue.

I forget the exact packaging of the watch and the charging puck. Have you removed all the clear plastic from them?

M1 Mac mini, macOS 13.5.2;  Watch, series 7 GPS/cellular, watchOS 9.6.2; iPad Pro 2nd Gen, iPadOS 16.6.1; iPhone 12 Pro, iOS 16.6.1; TV 4th Gen, tvOS 16.6; HomePods, audioOS 16.5 and Airport Express w/ Airplay 2

Try connecting it to an apple brick or an apple certified charger and see. Also, you can try a force restart:

To force restart your Apple Watch, press and hold both the side button and Digital Crown for at least 10 seconds, then release both buttons when you see the Apple logo.

I totally understand where you’re coming from, I am glad though that Apple did remove the chargers from the packaging, as the boxes are now smaller for one, and for another I have those chargers EVERYWHERE from all the Apple products that I have purchased when they did include them and I didn’t need them because when turning them in or whatever it was never required to turn those in as well so I kept the new ones as backups. Should have an option to get it included or not at a discounted price. However, it doesn’t necessarily have to be Apple’s version, there are plenty of 3rd party options you can use as I don’t even use an Apple power brick for that because I have a station that charges everything with one plug and looks a lot neater but I get it you don’t have one of those either the situation you’re in, Just giving you some options but that is most likely the cause of your frustration as to why you’re having the issues you are.

AFAIR, Apple has never supplied a charger for the Watch. Apple assumed that you had one for your iPhone.