> in the US the early eight-bit home machines gave way much earlier to consoles

That’s my understanding as well. In the US the NES was huge in the late 80s, but in the UK home computers were dominant. The NES never sold well in the UK.

The 16-bit consoles did later on, though. So did the 8-bit Sega Master System, but not until the early 90s - it wasn’t a predecessor to the 16-bit machines, but a budget-friendly contemporary.