The association is wrong. Gunpowder weapons appear in the middle ages,
OK, historical background, the beginning.
1. Gunpowder did not appear in medieval Europe. It was imported into the European Middle Ages from a much more developed region.
2. At the same time, in any civilization there is always a set of high-tech, which is unsuitable for mass replication or / and significant use due to limited efficiency, high cost, etc. As an extreme case, breech-loading and magazine rifles (with lever reloading, almost "Winchester"), breech-loading guns with a wedge bolt, oblong projectiles with remote detonation, revolvers, etc. appeared in the 16th and 17th centuries. Quite a glamorous look and clearly not the first revolver – this is the 1580s, "Winchesters" - the 1630s. Moreover, even magazine guns were rare weapons, but not an isolated one.
However, it's still exotic. A much more illustrative example: rifled weapons, invented in the 1490s, generally had a limited presence in the army for a very long time, but in noticeable numbers and constantly.
In general, recklessly using the logic of "it has already existed", we can assume that nothing new has appeared since the 1630s and before the invention of the machine gun. Although ... there is information about a certain English patent for using the energy of powder gases for recharging - the 17th century, yes. In general, only aviation, only hardcore.
That is, it is necessary to distinguish between phases 1. ideas, 2. experimental single samples, 3. limited and not seriously affecting production, and 4. the appearance of "practical" samples. Which, after distribution and testing of the application, have a significant impact on the situation. In the case of interest to us - on the course of hostilities.
So the effectiveness of the use of gunpowder in the Middle Ages and after 1440-1450 was very different. In reality, the conditional "renaissance" is the era of dominance of a very specific gunpowder weapon. At the same time, you clearly underestimate the "small" problems of gunpowder technologies of the 14th - first half of the 15th centuries.
Let's say another 1400 is
1. non-granulated gunpowder (powder pulp) with all its funny features. It is a) inconvenient when charging b) hygroscopic and had to be constantly dried, risking being blown up in the process. Moreover, the ideal control of dampness is difficult and the characteristics of the pulp "crawl". But these are minor drawbacks against the background of the fact that it has disgusting ballistic characteristics and therefore a large and expensive pile of rapidly dampening gunpowder is needed (almost twice as much as granulated). And even in dry form, the characteristics of the pulp are unstable – the strength of the shot depends on how optimally it is rammed. Too tight and not tight enough = the strongest deviations in the power of the shot. In general, when shooting with an accuracy slightly higher than "that way", there is no such thing as a rate of fire at all. Even if there is time for accurate shooting, a very high qualification and a "real" gunner is required - one for a dozen guns. With the slightest lack of qualification, the accuracy drops outrageously.
2. All guns that look like artillery, not an enlarged "hand cannon", shoot mostly stone cores. In other words, these are a) time-consuming ammunition to manufacture b) with low strength c) a very poor diameter-to-weight ratio. B and C require a large caliber, which... provides rapid braking in the air. Which requires an even larger caliber to preserve the impact force.
3. At the same time, the guns of 1400, except for small ones, are forged from iron strips. That is, in the first approximation, the gun will be either flimsy and short-range, or very heavy. That's all, you can forget about normal field artillery. What could maneuver has a negligible firing range.
4. However, in any case, there are no normal carriages ... either. As a result, about the same thing is put on the wheels that exists in the portable version. At the same time, the price of the issue turns out to be ineffective guidance - by tilting the entire carriage. An alternative option is to put a slightly larger cannon on a "very mobile and passable" wagons.
5. At the same time, the problem of sieges is not only that a suitable cannon will be very heavy and not long-range. The problem is that the tool forged from iron strips at that time cannot be made both durable and large enough. The bombard of 1400, often with a huge caliber, is the so-called bombard-mortar, 3-4 of its own caliber in length. With efficiency against high-quality fortifications, everything is very bad.
Now let's look at the handgun. There are already shooting things on sticks, but…
1. The gun lock has not yet been invented. One hand is occupied with a fuse when firing, and SUDDENLY it is impossible to hold a weapon and aim with two hands. As a result, "manual guns" are either low-power, or require four hands (a "crew" of two people), or not very manual, because they require shooting from a stop. In other words, at least some powerful individual weapons can be used mainly from stationary or semi-stationary positions of the "Hussite cart" type.
2. We have the same powder pulp, which is especially fun to hammer a long barrel of small caliber.
As a result, an individual firearm looks like a cheap ersatz crossbow. As a result, until the middle of the 15th century
1. rare hand guns in field armies were lost in the crowd of crossbowmen. If there are any at all. Already in 1432, in advanced Italy, a rich city hires a condottiere... and there are zero handgunners in the squad with the same crowd of crossbowmen. For comparison, in 1482 (the age of the arquebus), following the results of another war, Milan exposes crossbowmen to the door, replacing them with firearms infantry.
2. and next to the bombards, throwing machines are quite thriving.