I had that lens briefly and found it slow to focus, frequently missing a bit and sometimes just sawing back & forth without a lock - on an A7III. I know some find it OK, but it was probably the worst AF experience I've had since the 1980s. If you can, I'd try to send it back & pick up the kit 28-70 for similar money for general shots, because it's simply much better unless you need a large aperture/shallow depth of field/super-sharpness.
If you've been using a 50 on the 6000 then consider the 85 f1.8 for low weight a super-quick focussing at reasonable cost.
On an A7 it wont be the lens holding it back, it will be the camera. Even with the fastest lens the A7 cant compete with an A6000, especially in AFC.