My question is if in a tube preamp to solid state power amp scenario, the damping factor would be dependent solely on the power amp?
It is a little more complicated than that. Even though preamps have nothing to do with damping factor directly it has an indirect effect. To take full advantage of all the damping your power amp is suppose to provide you need a preamp which is appropriately matched. One of the reasons why impedance matching between pre-power is so important is again this.
To illustrate, considering that one has a power amp with an input impedance of 20 kohm, in general
keeping everything else constant, a preamp with an output impedance of 100 ohms will present a much cleaner tighter bass than a preamp with an output impedance of 1000 ohms. Basically the preamp with higher output impedance is not driving the power amp well enough to make its full damping factor available for delivery. These data normally is prescribed by the power amp manufacturer.
There is a general indicator that the ratio of output impedance of the preamp to the input impedance of the power amp should be 1:10...but please note that this is the
least ratio to be maintained. A ratio of 1:100 is much better and desirable to start with.
Unfortunately tube preamps present a notoriously high output impedance than their solid state counter parts. For example a Shindo Aurieges preamp present an output impedance of 2000 ohms which is very high. An ideal match for this preamp would be a power amp with input impedance of 200 kohms and above. You would not find many such amps. You CAN use a power amp with low input impedance to the tune of 40 kohms but you are not using the full potential of the power amp when it comes at controlling the driver (what you call DAMPING FACTOR) with this tube preamp. There are ways to build tube preamps with low output impedance and high drive but they are normally expensive and therefore rare.
An Einstein tube preamp present an output impedance of just 50 ohms, the reference tube preamp from Octave Audio has an output impedance of 30 ohms...super!! There are more.
But all these are very expensive.
There are other matching criterion like input sensitivity, input capacitance etc but impedance is the first thing to look at.
So, Damping factor also depends on the preamp, though indirectly.