Is one router enough for the whole house?

The networks are not completely separated, there are a few precautions and separate IP address ranges - open would be different. If an employer sets up a home workspace, they are responsible for security, not the employee. I am self-employed and also take responsibility for my own risk.

With all due respect, if you go into the MM with this prior knowledge and ask for two routers, the chaos will be perfect. Two routers without proper configuration only cause problems. As already mentioned, you are probably confusing something. A router initially has nothing to do with WLAN. What you probably mean is an all-in-one box like Fritzbox or Speedport. They cover several functions. Technically, they are modem, router, and WLAN access point all in one. If your two residential units are not connected (i.e., network cable-wise), then it won't work. Or rather, it's a lottery how much WLAN arrives. If they are connected, then as previously said, access points are the solution. One router (e.g., one Fritzbox each) per apartment will only cause you problems without knowledge of how they must be configured. Unless there are two independent Internet connections.

I now out myself as probably the user with the simplest and most primitive internet configuration here in the forum :D

We have a "router" (Fritzbox 7590) in the living room and a simple repeater on each of the three floors. The speed ("Highspeed") of the connection is specified at a maximum of 60 MBit overall (and that only for about 18 months). For us (!) this simple - and certainly primive(st) - configuration is 99% sufficient. On all floors, streaming can be done simultaneously - even in HD :) - although two of the TVs are connected via WLAN.

In a new building, I would certainly choose a different configuration.

But should not be used as an example ;) with 4k it can already be tight. Such a solution is only suitable for old stock if you cannot/will not pull cables…

We have a wooden house with cellulose insulation. The walls greatly dampen the WLAN signal - it is not just reinforced concrete. Modern construction is WLAN unfriendly. The question is not whether, but where LAN connections will be installed. At the latest when children become teenagers, purely WLAN repeater-based coverage will very likely lead to unpleasant daily discussions. In addition, the WLAN standard is not being improved in terms of range (radiation regulations), but applications are increasingly consuming bandwidth (this trend has continued for 20 years and shows no sign of ending). A brief look ahead puts the LAN installation costs into perspective.

Should not be used as an example ;) with 4k it can already get tight. ...

Just last weekend I watched Suicide Squad in 4k, while my wife indulged in Rosamunde Pilcher (HD) and the child immersed in Riverdale (HD)... Home schooling and home office could also be carried out satisfactorily in recent months. But as said/written: In a new build/purchase I would certainly choose a different configuration. Safe(r) is safe(r)