What would be the impact of my magic system on technological development of human-like civilizations, starting with bronze age level technology and going through to around 1900 level technology (through all this time, no one knows how magic works).
Magic consumes energy from special ATP generating cells that have no other functionality. It can only turn the ATP in those cells back into ADP and a phosphate, using the energy that results with 100% efficiency (or maybe less, as described later). It can not farther break down the ADP into AMP. It also can not use ATP in other cells, so trying to expend too much energy will not kill a person by depriving vital cells of energy. While all people have some amount of these cells, a person's magical ability is determined by the number of these cells (a person with only a few of these cells will not be able to work much magic at a time, but a person with many of these cells can do a large amount of magic).
The energy consumed by the magic would be the same through accomplishing the task through purely physical means at 100% efficiency if the magic is working within 100 yards of the person casting the magic. If the magic is doing anything beyond that range, it will increase in energy with the square of the distance (120 yards is 1.44x energy, 200 yards is 4x energy, etc.), with the waste energy turning into heat (more on this later).
Matter, energy, charge, linear momentum, and angular momentum are all conserved by magic (except for the matter and energy when magic produces matter from energy, where E=mc^2). Any change in charge caused by the magic with result in the body of the person who casted the magic gaining an opposite charge. Linear and angular momentum similarly impact the person casting it. Note that all three will be equally spread out through the person casting it (so high g-forces during the acceleration will not kill or injure the person, though it can put the person in a situation that can harm them) and that, if the person does opposite magic that cancels out the change in those 5 (i.e. giving one object a strong negative charge and another an equally strong positive charge) this will not impact the person.
If the spell works on something farther away than 100 yards, the waste energy heats the person up, so trying to do too much too far away will, if you don't run out of energy first, cause you to overheat and die.
If the spell you cast would start with input energy and produce more (such as an exothermic chemical reaction), you have to input the starting energy and you will not get any of the released energy back as ATP.
The other limiting factor on what you can do with magic is what you can think of doing. Creating a fire would not require any knowledge of how fire works, for example, but it would require knowledge of the existence of fire. Cutting a person's aorta in an attempt to quickly kill them would require knowledge of the aorta's existence (and would not be attempted unless the person casting the magic has knowledge of the aorta's importance).
If a person attempts to cast magic to accomplish something without thinking of how the magic should accomplish it, the magic will automatically use the lowest energy way of achieving it. For example, trying to start a fire will not result in sunlight being focused from near the sun because, as it is so far away, it will take an absurd amount of energy and kill the person many times over with heat.
If a person casts a magic spell to do something, while another person casts magic to prevent it from happening, energy is drained from both people until either one person runs out of energy or gives up on casting the spell.
Casting a magic spell is done entirely mentally and, as such, will only cause what the person meant to happen to actually happen. There are no side effects of magic aside from what has already been mentioned.