How is etalon important to tunable lasers?
Tunable lasers utilize some kind of feedback in order to maintain the same optical intensity.


This is not correct. In fact, lasers do involve feedback, but it is a positive feedback mechanism, not negative feedback. That means that the feedback is not what maintains the optical intensity.

Lasers are essentially optical oscillators. There is a positive feedback mechanism  and a gain mechanism that work together to sustain an oscillation. The feedback mechanism tends to cause the output power to increase exponentially without limit. However the gain mechanism is only able to support as much power output from the laser as is put into it in the pumping process. So it is the gain mechanism (or gain medium) that maintains or limits the laser's output intensity, not the feedback.


  I've read that there is some kind of etalon trans-impedance amplifier that works in order to generate the output necessary for this feedback.


Again this is incorrect. An etalon (as the term is usually used) is simply two flat reflecting surfaces parallel to each other. Light reflecting back and forth between the two surfaces of an etalon is one possible way to set up the feedback mechanism to produce a laser. However, practical lasers more often use either curved mirrors or more complex optical arrangements (waveguides in the most common types of semiconductor laser) to minimize diffractive losses and increase the laser efficiency. 

Also, an etalon is not an amplifier. The amplifier in the laser is usually some other material placed in the cavity. For example, it could be a piece of semiconductor, or certain other types of crystal (ruby, for example), or a stream of dye-bearing liquid. 

Also, the amplifier used in a laser is not a transimpedance amplifier. A transimpedance amplifier is an electrical amplifier, but a laser requires an optical amplifier.


  I'd like to know how the reflecting surfaces of the etalon generate the analog signal that is necessary for feedback.


Now, how can you set up a laser to produce a well-controlled output power? We could simply limit the input pump power to the laser. But then, if the laser's efficiency drifted (which it will do, due to temperature shifts, etc), the laser output power would change. 

What we can do is pick off a small portion of the laser beam, either from inside the laser cavity or from the laser output, and direct that to a photodiode. Then the photodiode output can be used to control the pump power in such a way to maintain the laser output power. The etalon (if the laser has one) is not particularly involved in this control circuit.

In this case, the control circuit would normally be a negative feedback circuit. And almost universally, a transimpedance amplifier would be used to convert the photodiode signal into a voltage that can be amplified in the rest of the control circuit. 

But the details of the control circuit are entirely under the control of the designer. There's no fixed designs that are used, or that are applicable to all kinds of lasers. The control circuit would be designed to account for the dynamics of the laser action, the kind of control signal needed to control the pump mechanism, the required stability of the output intensity, etc. 

Tunable lasers

So far I haven't even talked about tunable lasers. Everything above applies more or less to any kind of laser, tunable or otherwise. 

But tunable lasers get even more complicated, because you want to control not just the output intensity but also the wavelength. In this case, if the laser cavity is formed by an etalon, shifting the spacing between the etalon surfaces can be a means of controlling the wavelength. In this case the etalon is an actuator that sets the wavelength, it is not a sensor that tests the wavelength, and it is not an amplifier.

It would also be possible to use a (second) etalon outside the laser, in a second pick-off beam, to test the wavelength and use that to drive a feedback mechanism to tune the laser. Here, the etalon would be used essentially as a narrow-band band-pass filter to detect whether the laser output wavelength matches the desired wavelength or not. A photodiode after the etalon and additional amplifier components would be used to convert the etalon output into a signal that could be used to adjust the laser tuning mechanism.

In either case, the tuning range of an etalon is quite small, and their use as either tuning mechanism or in the sensing path would be limited to cases where only very fine adjustments to the laser wavelength are required.