First, I would actually measure your numbers. Because I find 15l of water in the pipe to be non-believable. That's 100m (300'+) if the pipe is 3/8" trade size, 60m (200') if 1/2" pipe, and 35m (100+') of 3/4" pipe, but 3/4" would be a dumb choice because it has a huge inventory of water, which means a ridiculous wait for hot water.
If your house really is that big, a single water heater for the whole house is impracticable.
Your tank needs to be pretty big, though.
Here's the thing. As your tank refills, it's going to be filling with cold water. Hot water tanks are specifically designed to separate flow. So for the first 2/3 (20 lit34s) of water, you'll take that off the top of the tank and it'll be tank temperature. But with only 10 liters of old water left, what's in the tank? 15 liters of cold water from the pipe, and 5 liters of actually hot water that has finally made it through. Let's say the pipe lives at 10C and you want the water at 40C. Half the water in the tank will be 40C, and the other half 10C, now mixed together because the separation is no longer working. What temperature will that water be? That's right, 25C. Barely tepid.
And it will be like that for the next 20 liters of usage. Then for the following 30 litres or so, it will slowly blend to warm up bit by bit.
This will result in an annoying "mid-shower cold lump" that will probably just motivate you to take Navy showers lol.
But let's do it again with a 120 liter tank. Now your first 80 liters are fine, and the first 15 liters of cold water will have plenty of time to diffuse into the last 40 liters remaining.
Temperature will also help.
You seem to want to run the hot water system at very close to desired final shower temperature. That is dumb. You want to mix significantly hotter water with cold water, so you have some headroom for variances in hot water temperature. (This might be a big part of why you need to run 15 liters of water to be comfortable).
Ideally, you want an automatic mixing valve, which will automatically adjust out these hot water temp variances, and also provide anti-scald protection. Anti-scald protection in turn allows you to run the tank hotter still, which further stabilizes spigot temperature.
But much more importantly, hotter tank water allows the tank to stop dangerous bacteria growth - a phenomenon only recently understood, because fatalities from it happened sporadically and randomly. When Flint, Michigan made abrupt changes to their water supply, among other things it triggered a large enough cluster of cases to become detectable! Investigation ensued and found low-temperature water tanks festooned with legionella and other bacteria. Before that, no one knew!
Now if you don't want a clunky "hotel style" valve, I hear you. They make much better thermostatic mixing valves which allow 2-dimensional control of flow and temperature - like a joystick. Sometimes flow is an ungainly push/pull, but temp is a fine control knob that can be simply left in the desired position.
But if you really like two valves, thermostatic mixing valves can be plumbed in right before the hot water tap. This will mix in cold water as necessary to keep the the hot water tap right on target temperature. (and prevent scalding, of course).