Turbo lag is normal, but is is rarely more than a couple seconds. Even my F350 when pulling a heavy trailer I don't notice it - unless I'm in too high a gear for my speed. (I've only had a turbo with a manual transmission - I've driven some automatics that are slow enough to shift that you might think it was bad turbo lag, but those cars didn't even have a turbo)

I think it's mostly transmissions and other non-turbo effects that cause these contemporary lag complaints.

With all the fleet mileage requirements, there are much higher gear ratios for cruise and coast modes, so the engine can be bogged way down near idle speeds. Also, there are more software based throttle controls and interlocks. Some of this has to do with heavy-handed reaction to prior "unintended acceleration" panics, and some is just part of all the modern traction/stability control and efficiency programming.

The programming can get utterly confused and fail to dip back into a ground state where it is ready to accelerate. People doing various combinations of heel-and-toe or other transitions between braking and acceleration, including rolling stops, may get their car into a different mode than they would want, and the recovery from this seems like "turbo lag" or worse.

I wouldn't say that is a thing anymore since the 1980s. My old 2003 truck a 5.9l turbo diesel was quite responsive but at nearly 6 litres spewed a lot of exhaust to spin up the turbine. Smaller cars may suffer a bit more although some sporty cars may have two stages; separate small and large turbos. The small is good at lower rpm and the large better at high rpm.