I have the A7iv and LA-EA5 adaptor, so hopefully my experience will be useful.
I upgraded from an A900 to the A7iv (and still have my 2nd A900 as a backup, so have been able directly compare).
Lens wise, I have just 1 e-mount lens, the Sony 200-600 G (I did have a Tamron 150-500 USM on my A900, but traded that in when getting the A7iv, figuring that was the lens that would most benefit from faster AF with a native lens - and I've not been disappointed, the 200-600 G is superb)
In terms of A-Mount lenses, the performance in terms of AF appears to be down to a given lens having in-lens AF motor or using the in body motor via.screw drive.
All the lenses I have with in-lens motors work flawlessly, smooth and fast (as was the case on the A900), plus taking advantage of the fancy AF features the A7iv offers.
The two screw drive fast primes do work, but as not as fast or smooth as they were on the A900 - I suspect this may be simply a case of the A900 having a very powerful AF motor (to the extent that it has an option to operate it on reduced power if you have older 3rd party lenses to avoid the high torque damaging the gearing in the lens), and the LA-EA5 having a less powerful motor.
I have the following lenses:
With In Lens Motors
Sony CZ 16-35 f/2.8 SSM
Sigma 24-70 f/2.8 HSM
Tamron 70-200 f/2.8 USD
Sony 70-300 G SSM
Screw Drive AF
Sony 50 f/1.4
Minolta 85 f/1.4 G RS