Are there any bike light sets that don’t rely on the o-ring design to attach them to the frame?
Yes, there are. Any decent StVZO compliant light from any quality German manufacturer can be attached not only to handlebars but to also the fork crown. None of those attachments rely on O-rings as that would be stupid. The whole idea of StVZO is that the headlight beam pattern must illuminate the road but not make oncoming drivers and riders blind. Thus, the headlight angle needs to be very carefully adjusted. With O-rings, that adjustment would not stay set as a minor touch to the headlight such as to remove a battery headlight from the handlebars would alter the angle.
The very best of the lights are powered by a hub dynamo (on a regular bike) or the e-bike battery system (on an e-bike -- it would be ridiculous to convert e-bike battery electricity to forwards motion and then re-convert the very same forwards motion again to electricity on a hub dynamo).
Many of the hub dynamo lights have a standlight so you get light for 4 minutes after stopping. Also quality hub dynamo lights don't flicker like the cheap ones do. You may also find many lights available with an automatic environmental brightness based sensor to toggle on and off the light based on ambient light level.
I think you'll find that some of the lights are powered by a battery. They are a poor solution. They need constant recharging and you need to remove the light every time you leave the bicycle locked so it won't get stolen. A hub dynamo light does not require recharging and is unlikely to be stolen.
Also if your fork crown has fender/light attachments, you want to attach the light there. The reason is that the lower the light is, the more shadows obstacles make so with a low-mounted light you are more likely to see hazards on an uneven road. Mounting it even lower, on a fork blade, could be done but then your wheel makes a nasty shadow on one side so that's not preferred. So that's why all quality lights attach to the fork crown as a first option and the handlebars only as a second option if the fork crown doesn't have the attachment point.