How do Schengen countries know if someone has overstayed internally?

Enforcing this very strictly is not a priority. There are ways to know (asking neighbours, looking at financial transactions, rent agreements, local police noticing your car a lot, etc.) but I don't think they are used a lot. In some countries, hotels and other commercial accommodation providers also have to check their guests ID but that's not the case everywhere and I suspect those data are not used systematically either.

The main point of the rule is what it doesn't do: you don't have the right to live in another Schengen country, take up employment or avail yourself of public help. In that context, the 90-day threshold is just a pragmatic definition of where visits ends and residence starts, which happens to track the limit between Schengen short-stay visas and national long-stay visas.

Note that entries and exits from the entire Schengen area are not recorded in the SIS either (there is another system for that, which hasn't come online yet). That's what stamps are for but that too isn't enforced very strictly. We are getting used to the notion that states should use computer systems to check each and every traveller's comings and goings and that staying 91 days is a very serious offense but it isn't how immigration law worked until the 90s and simply isn't how most laws work even today. You don't need enforcement to be systematic and automated for a rule to have real effects or be useful.

On the other hand, if you attract negative attention to yourself or you're found working (illegally) on a construction site or in a restaurant, all these rules make it easier to remove you. That's how many immigration violations come to the attention of the authorities in the first place and was until relatively recently the only enforcement priority in many countries.

Within the Schengen area, they usually don't know. That's the price to pay for having low-friction travel over the internal borders.

• Any attempt to work illegally could come to the attention of the fiscal authorities.
• Similar for formal education.
• The lack of a presence in the country where they are supposed to be could cause problems, e.g. for a job or student visa.

That leaves the option to get a weekend cottage and to stay there all the time. The Schengen countries are willing to take that risk.

Schengen doesn't register entries/exits electronically - SIS certainly has nothing to do with that.

It is through entry/exit stamps that overstays can be detected, though not all border agents are scrupulous about checking them.

When travelling within the Schengen Area, no stamps are issued, so there is indeed no easy way to check if the 90-day rule for residence permit holders has been respected or not.