On my powerbook (17" late 2011) BOINC uses more power than the charger can deliver.
In the end even though the computer is connected to the charger, battery level will fall until MacOS shuts down.

I know, the charger might be a little bit weak, nevertheless it is a general problem with high performance laptops, there are some which can't charge as fast as their peak performance would demand.

So my question is: Where's the button or setting to prevent BOINC operation below a certain battery level like on any android device? Is there any? And if not, why? On mobile phones there is such a setting.

My current workaround is to reduce CPU time and core count to a percentage where my battery isn't drained. Drawback is, this usually works only for a single project as power consumption seems to vary vastly depending on algorithms.

It could also be that your battery is no longer charging fully. Batteries have finite charges, eventually there comes a point where loading is slow or a total no go.
Especially Apple had a software trick on iOS devices where the battery would load slower, eventually the whole device would go slower, to force you to update to a newer device.

No, BOINC for MacOS does not have a setting that stops itself when the battery becomes low.
If you want to, you can ask the developers for it via https://github.com/BOINC/boinc/issues

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In my case I think the power supply is a little bit damaged due to ageing, but it is not uncommon for chargers not performing optimal e.g. when using a travel adapter and a different AC voltage etc.

I swept through the forum on github and found, there's already a long term feature request. Hence I have to wait.

https://github.com/BOINC/boinc/issues/1758

it is queued here:
https://github.com/BOINC/boinc/milestone/14

You have my sympathy.

I have a Surface Pro 4 with a weak charger. I looked at Best Buy into a docking station but specs said it could not be used to charge through the USB3 ports while attached to the surface pro. Best buy did not carry a charger for surface pro as it was proprietary. I asked at the microsoft store and they said I had to get a charger for the "surface book" if I wanted a heavy duty charger for the "pro"

It is generally not advisable to run boinc on a laptop, as the load and heat can severally shorten the lifespan of your laptop.
Not saying that it will kill it, IMHO and my own experience, it's put some older hardware in an earlier grave.,.
But it you really need to run it on a laptop or any hardware for that matter, you can choose to use less "CPU TIME".
In the Boinc menu choose tools, computing preferences, see other options and in the USE AT MOST line choose to use say 75% or 80% CPU time.
It will give the CPU a break at time to cool a little the lower the percentage the less it will work it and more time to cool and save power.
CPU at full throttle all the time uses more power and creates more heat.

On another note: if your battery is over 3 years old and is used with adapter plugged in most of the time, or has many cycles on it, may be time to invest in a new battery. You can also choose less COREs if you have multiple cores 100% is all
50% would be 1 core in a dual core etc.

I used to run BOINC on a older Thinkpad. Lenovo has their Power Manager software for the laptop. When I started running BOINC I noticed the battery would drain out. I eventually discovered that the Power Manager had a "hybrid mode" that was enabled. When I un-checked it, I found the battery level would stay charged!

You very well could have old/faulty hardware as others have pointed out, but look and see if this option is available for you to play with. If you haven't done so already, make sure to put your laptop in performance mode as well.