I don't know of any thermostats that aren't part of a proprietary system involving communicating thermostats that will control the speed of the fan, other than on or off. My furnace also has a variable speed blower, however the ecobee has a setting that will allow the HVAC system to control the fan speed. Generally this is the best choice when using something like an ecobee or nest in systems with variable speed fans. Assuming you're not using a communicating system, are you sure this isn't the way your system is already working with the existing thermostat? Generally fan speed behavior that's controlled by the HVAC can be adjusted with dip switches on the furnace control board.
I am not sure about any of that but it is something I will look into. Right now I have these around the house in various locations.

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