What if the black hole in the center of the galaxy grew faster? Imagine that hypothetically the black hole in the center of the milky way gradually increased in mass by for example 50% every year. That is exponential increase in mass.

Which visual effects would we see on for example Alpha Centauri, stars more distant and on M31? Red or blueshift? Lensing?

How about linear increase in mass?

Are there software I can use to visualize it as seen from earth?
this is not really an answer to your question, but to the assumption you made.

The BH in the galactic center cannot grow that much. There are two problems. First, there is not enough food close by. Any potential food (gas clouds, stars, and dark matter) will have some non-zero angular momentum preventing it from coming close enough. Loosing this angular momentum is difficult (it cannot be radiated away like energy), the only way is to exchange it with other objects either via impact (of gas clouds) or gravitational interactions with other objects (not the BH).

The second problem is that a feeding BH is surrounded by an accretion disc of hot gas. In that disc, angular momentum is slowly transported outwards and mass inwards via viscosity (that viscosity most likely originates from turbulent magnetic fields that become unstable -- the magneto-rotational instability). This process inevitably heats the accretion disc to very high temperatures ($10^{6-9}$K) such that it emits a wind of raditation and particles (similar to the Solar wind, but much much stronger). If the BH feeds too much, this wind becomes so strong that it pushes away any further infalling material (potential food).

This second process limits the growth of any BH to double in mass in no less than about $10^6$ years, I think (I'm not too sure--if you want a precise value, consult the literature), even if the first problem was no issue.