The charger uses wireless charging to charge the battery in the toothbrush. The same principle is used with some mobile phones (Qi charging).
If you have a multimeter, coil some wire and put it where the toothbrush sits on the working charger. You should be able to measure an a.c. current across the coil. It should make a compass twitch too, maybe even a paperclip.
Given that the charger plugs directly into the AC mains power supply there most probably is a fuse in the charger so this may be the first thing to check.
The hard part in trying to repair the charger is access without any or very little damage to the case or the components inside.
Looking at images of the charger it appears that it is in a molded plastic case with no apparent seams. No doubt this it to make it as waterproof as possible given that a wet toothbrush could be placed on it.
If there is a seam on the case, try placing a sharp wide bladed tool e.g. a sharpened 1 1/2” paint scraper, along the seam and give it a short sharp tap with a hammer. Usually this will break a plastic welded case along the seam line with minimal damage
If there is no seam then you would need to somehow cut open the case, without damaging the internal components and then start checking the circuit board components inside.
If you could do this without too much damage then it may be possible to repair them but they would then need to be resealed and made waterproof again to be able to use them again in the usual place.
If you still have all or most of the old non working chargers then perhaps you could try and experiment to see how difficult it is and what the actual problem with them is.
If you decide that you might try doing this create a guide while you’re doing it. Others in the future will thank you. Here’s how to do it on ifixit Creating a Repair Guide