I’d like to find an ST-compatible switch with the following features:
On/Off controllable via the switch. This should power or unpower the circuit, at least if there isn’t a connection to the hub/bulb.
Dim function controllable via the switch should trigger Hue bulb dim function.
Other triggers should be able to toggle the switch, and thus the light, on or off.
Is there anything that supports such functionality?
A dimmer switch, smart or dumb, should never control the current to a smart bulb. The two devices will confuse each other, and it is likely that you will eventually burn out either the switch or the bulb.
You can use a smart dimmer switch with dumb dimmable bulbs, no problem.
Or you can use A smart dimmer switch that works by sending instructions to the hub which then sends instructions to the bulb. That smart switch can either be battery-operated, or just on a different circuit.
Some people do hotwire the connection to the smart bulbs so that the circuit is no longer controlled by the switch, which is another option, although then you will not be able to turn the bulbs off if the home automation system is not working.
Toggle switches and Smart Bulbs
You could also use a smart switch which just toggles, doesn’t dim, to control the current to smart bulbs, but the bulb manufacturers generally do not recommend that… They expect the bulbs to be always powered on.
There are two reasons for that. First, bulb life will actually be better if the current is not been cut on and off. Second, these bulbs act as repeaters for each other, so if you are cutting current around the house you may suddenly find that the bulbs which are farthest from the bridge no longer work. Or just some random group of bulbs stops working because someone turned off the wall switch in another room for a bulb that was being used as a repeater for them. The bulb network will work the best with all the bulbs remaining on, because it gives the most options for repeating messages.
Smart switch covers
one of the newest device types is a smart switch cover which leaves the original switch in place powered on (no wiring changes, and available if the home automation system fails) and places a battery operated switch over the top of it for intuitive control of any device Controlled by the network, including smart bulbs.
Detailed discussion
The following thread has a detailed discussion of various switch options for use with smart bulbs. Different ones will work for different people. 
I understand that I can’t simply regulate current to a smart bulb from a switch. I’m looking for a smart switch with a dimmer that functions by controlling the smart bulb(s), while retaining power on/off capability. It should also be controllable via zwave/zigbee/etc to turn the power to the light on/off. Is this something that exists?
Not that I’m aware of, and I follow the device certification announcements for both the zigbee and zwave alliances pretty closely.
There are some office equipment devices which hide an on off switch in a box underneath the network switch for emergency use if the network fails, but that’s not the same thing.
AutomaJohn, are you essentially looking for a replacement wall mounted wired switch that can control the flow of power to the Hue bulbs via the wall mounted switch which in turn can be controlled via the standard Hue wireless switch interfaces, or app?
I’m in a similar boat. I have philips hue lighting and a hue bridge, and a wired switch that turns on a gas fireplace. I don’t want to replace the fireplace with a dimmable smart bulb; I want to replace the switch with something so I can control it along with my lights. Is there a way to do this, without buying an additional hub for some other standard?