You're right!
Try using another charging cable and/or charging brick. And if that charges the watch to where you can check your battery health--great!
Personally, this exact issue happened to me and it ended up being the charging cable. It took me a few tries to figure it out--first tried a different wall out with the same brick & cable, then tried a different charging brick with the same cable, and finally borrowed a different cable with a different brick from a friend (which worked.)
So I used that cable with my own brick and the watch continued to charge--so long story short, it was the charging cable that needed replacement. Also checked the battery health once it was charged sufficiently, and the capacity was around 90% so I knew the problem wasn't the battery itself.
So it may take some attempts to isolate the problem.