At one end of the scale, if you're at the end of a long distribution line and the power is coming from an old gas turbine then it could be less than 15% from fuel in the ground to electricity in your home. Worst case, if the fuel was LNG used in an old open cycle gas turbine and it was a hot day and you're at the end of the line then it could be barely 10% efficient. That's an extreme though.
At the other extreme if you're standing right next to a hydro power station and that's the source of power charging your car then you're looking at 90% efficiency. Heck, even ye olde working museum (aka Lake Margaret power station, built 1914) achieves 80% efficiency.
Realistically though most won't be charging their car in the middle of nowhere during a heatwave and most won't be parking literally outside a power station either.
For the vast majority of thermal plant in operation in Australia the efficiency is in the range of 30% to about 37%. There's some below that (worst are down around 20%) and some above that (best is a bit over 50% for a stand alone fossil fuel power station) but the vast majority of power actually generated is coming from plants with efficiency in that range. That's the efficiency of the power station only.
Now take out the energy required to extract the fuel from the ground, process and transport it. How much that is varies hugely but it's typically only a few % thankfully.
Then take out energy loss in transmission and distribution. For a typical suburban house that's about 10% of what comes out of the power station is lost in transmission and, more importantly, distribution.
Put all that together and as a generic answer grid electricity is very close to 30% efficient from fuel in the ground to power in your home. Higher in some places, lower in others and it will also vary with time of day and seasonally but as a whole that 30% is typical.
So in the context of electric vehicle charging in Australia, 30% is a reasonable figure to use for the efficiency (fuel in ground to power in your home) of grid electricity although the actual figure will vary depending on circumstances.
As for electric vehicles, my personal view is that yes it will happen but not as quickly as many are expecting or hoping. We're a minimum 30 years away from the point where seeing any petrol / diesel powered vehicle being driven on public roads becomes unusual to the point that such a vehicle stands out among the rest.
People often look at devices such as mobile phones and extrapolate the short lifespan (in practice) of those to other things. But that tends to fail in practice.
Go stand beside any public road looking for cars from the 1990's being driven. It won't take you long to spot one, at least not unless you intentionally go looking in a wealthy suburb but anywhere else there's still plenty around.
There's still plenty of heavy industrial equipment from the 1980's in use today.
Those with $ to splurge might do it differently but in practice there's no shortage of major appliances being used in Australian homes which date from last century.
Overall, the turnover time for all this stuff is longer than many (particularly government) seem to assume.
Hypothetically there's a transition over the next decade so that 10 years from now all new vehicles are EV's. Do that and it'll be well into the 2040's when petrol consumption has fallen to the point that it's no longer viable to run a business based around selling it.
All that said, if you really go into it then you'll find that petrol and diesel have oh so many evils from toxicity through to terrorism. Even if there's no benefit to efficiency or the environment and we generate 100% of the power from coal that still beats petrol or diesel in many ways simply because it gets us off the oil addiction.