If we could embed tiny "water" wheels into our veins and arteries, what is the maximum amount of power we could achieve? Assume that they will work and won't malfunction or clog our blood. Also, we can make them any size that we want and put them as close together as we want. How much power maximum can be generated per day? Will it be a decent amount, or not even worth it?
Since all the power that you can get is provided by the heart, the absolute maximum power that you can extract is the power provided by the heart.
This page provides some estimates to the power provided by the human heart. Most of the estimates are in the 1W - 2W range, and the only outlier (5W) seems to have enough editions reporting erroneous data as to doubt its accuracy. I would stick to the 2W upper limit.
Now, if you begin obstructing arteries with water wheels, that power will stop being used to move blood, so blood will not circulate well enough. In this case maybe the heart will start to pump more often, injecting more energy/power into the blood, until it finally cannot stand it and fails.
Destructible Lemon is right: Even ignoring the problems you said to ignore, these waterwheels will cause heart problems by making it work harder, in exchange for a relatively limited amount of energy.
If you need to generate significant amounts of power via an implant, you are better off making said implant piggyback on the existing purpose of the bloodstream: a transport system for fuel and waste products. Blood transports sugar and oxygen to tissues that need it, and removes carbon dioxide and other waste products.
So you engineer a fuel cell that takes sugar and oxygen from the blood stream and reacts them into water and carbon dioxide. If you really want to get fancy, the fuel cell can respond to the body's hormone signals for 'conserve energy now', etc (like adrenaline).
Blood contains approximately 18 milligrams per deciliter of glucose. Burning glucose produces 14.2 kilojoules / gram (which is 14.2 joules / milligram). Assuming 100% efficient heat-to-electricity conversion, that's about 250 joules in a deciliter of blood. Here I find an estimate of the flow rate of blood to be about 5 liters per minute, or 5/6 deciliters per second.
So if this hypothetical implant consumed every bit of blood sugar in a person, it would get (5/6) * 250 = approx 210 joules of energy per second (the definition of a watt). Of course, the person would die in short order from exhaustion if you did that.
A highly efficient fuel cell could realistically get several watts of power - a few percentage points of the person's normal baseline amount available. Say, 10 watts or so. If the implant slowly scaled up its demands over time, it could likely go significantly higher; especially if the implant plays nice with the body's hormone commands to adjust energy usage, the body will become accustomed to this new demand on its fuel and exhaust systems over time.
Several watts of power is easily enough for most things you would want an implant to be capable of doing. And the person would suffer no real ill effects except needing more food than they did before.
I'd guess it will likely turn out to be as hard to design such a fuel cell as it would be to design water wheels without clotting issues, too.
SJuan provided a page and explanation why water wheels in the veins is a bad idea, in that you're simply taking energy from the heart, and forcing it to pump harder. They provided this page as evidence.
one quotation stood out to me in the context of this question: "The mechanical power of the human heart is ~1.3 watts. It takes a much higher rate of energy turnover (~13 watts) to provide this mechanical power, since the mechanical efficiency of the heart is very low (less than 10%)" (emphasis mine). While it is unreasonable to use up the actually utilised energy that is pumping the blood, i believe you get into much more plausible handwaving territory, though i'm not a biologist and i don't know how realistic this would actually be, when you're utilising waste energy. This technically isn't an answer to the question of water wheels, but i believe it is similar enough conceptually to count as an answer.
this is really not a large amount of energy if it were to be utilised for actually powering things. in the real world, kWh per capita per year values are in the thousands for regions which use power, according to wikipedia, whereas the kWh per year for one of these devices (which clearly corresponds to one capitum) is just barely above 100, for higher estimates of waste energy.
it's possible that it might be useful situationally for an operative who needs a remote power source, but if they wanted to use anything more than a flashlight or something they'd need a battery, which would imply that in order to justify having an implanted power generator would also need to be implanted (if it weren't implanted, you might as well swap out the heart generator with a solar panel), and also consider that they'd have to be on pretty long expeditions without access to chargers to justify not just carrying the battery (although i guess you could consider that sometimes agents are captured i guess, or maybe they consider the risks of being cut off from the rest of their allies by for example falling in a pit or something real enough to justify such a procedure.)
it's also possible that the people with the implants are opposed to generating power through coal power and such, believing it unethical, but solar power would be more reasonable, though you could ask a question about whether it's realistic for solar power to not be discovered in a society sophisticated enough for surgery and implanted tech. or you could just remove the sun, but that would also require a different question, possibly already asked.