It turns out that GBM with constant drift and constant volatility is not really used in real life. It is well known that volatility as well as drift may vary over time. Hence, if you want to use a model with time-varying parameters, you need to come up with a model to define $\mu_t$ and $\sigma_t$. There are classic models that use some mean-reverting process for $\sigma_t$, but then the estimation and calibration of parameters becomes really challenging and is often more related to some sort of art rather than economics. Finding a process for conditional drift is even more challenging.
The way, and whether, you use GBM differs depending on what you want to do. Indeed, vanilla option pricing for instance relies on GBM but you will actually reverse the pricing formula and back out the volatility (which is then called implied volatility) because you observe option prices. The drift used depends on how do you price the option. For instance, in the Black-Sholes framework, that is using risk-neutral probability, the drift is going to be the risk-free rate.
For investment decision purpose, like asset management, it is another story. If you are interested in pricing future stock returns (not a single stock but rather the S&P500 or any large index), there are other methods much more reliable than pure normal shocks to price. These models often relies on macroeconomic variables, and in particular consumption, that helps gives a better view of stock prices (although there are also some problems with these methods).
If you want to price a single stock, you won't use GBM neither. Indeed, as you suggested the fundamentals will be too important in that case to simply use basic GBM. Again here, you will try to use alternative methods that relies also on macro data, like some sort of variation of CAPM model.
Regarding your initial question, yes, in theory you could be able to infer some GBM calibrations with company fundamentals but I guess this is rarely used in that way.
Overall, I would say that GBM is not that used by anybody because it is the most basic model you can come up with, and have several large limitations in its "usual" form : constant mean and variance. There are strong evidence that the mean and the variance are not constant over time.
