Manual focus (MF)
To be honest, I've only really bothered with manual focus when shootings static subjects at very large apertures or sometimes when taking landscape photos. But with the focus peaking feature - that highlights the subject(s) in focus - manual focus is a delight to use. This makes me more inclined to use some of my adapted vintage MF lenses on the Sony A7 III. Additionally there is also a DMF mode (Dynamic Manual Focus) which is a hybrid between AF and MF: you use autofocus to gain a general focus and then seamlessly finetune the focus with manual focus - again, with focus peaking. This is such a neat feature.
EVF (electronic viewfinder)
Now, this is a subject where opinions are often divided. I've always enjoyed using optical viewfinders (OVF) and the first time I looked through an EVF (on an Olympus) I was not impressed. That being said, there has been noticeable progress with EVF's the last few years.
The main advantage of using an EVF is that you get a live preview of the exposure and depth of field of the image you are about to take. (Both on the EVF and on the screen). If you are a night shooter you'll love not having to try to compose your shot in a completely pitch black optical viewfinder!
Having a live preview in the EVF also allows you adjust your settings on-the-fly without having to take a photo, look at the screen, adjust and retake. This brings me to the next advantage of an EVF over an OVF: you can review images you've just taken directly in the EVF meaning you won't have to take your eye away from the viewfinder to look at your LCD display. This is actually a lot nicer than I had expected it to be. Plus if you're outside in super bright conditions, it's usually far from ideal to review images on an LCD displays - so doing it in the EVF is a great alternative.
The only real annoyance I have with the EVF on the Sony A7 III, is that there is a slight lag, from when the camera detects that you've put your eye up to the EVF, until it activates it. We're only talking about half a second or so, but when you're used to using optical viewfinders you will notice that it's not instantaneous. I hope Sony will address this in a future firmware update(?)
Worth noting: the sensor that activates the EVF seems to be well-calibrated. If you've flipped out the tilt-screen and, for example, you're shooting from the hip, your body won't accidentally activate the EVF and cause the LCD screen to black out. Candid photographers will love this.
My final note on the A7 III's EVF and LCD screen is that they are of lower resolution compared to its older siblings - the A7R III and A9. This does makes sense, seeing as Sony had to cut costs somewhere to keep the price reasonable - and this is one of the few places they did so. To be honest, it would be nice to have crisper displays, but at the end of the day, this doesn't affect the camera's capabilities or image quality.
Battery life
The battery life of the new Z-battery is very capable. If you've read my first blog post, one of the major issues that kept me from switching to a mirrorless system was the subpar battery life. No way was I going to carry 4-8 spare batteries on me - the very idea of it was ludicrous.
Sony has now addressed this with these new batteries and I'm happy to confirm these will last you a full day and more. I've purchased one spare battery and cannot think of any scenario where I would need more than two spare batteries. Additionally, the battery can be charged in-camera, so in a cinch you can extend your juice on-the-go with a powerbank. Reportedly, the A7 III also manages power better than the more expensive A7R III and A9 (perhaps due to the lower res EVF and display?) and therefore will give you slightly better battery life than its elder siblings.
The Z-battery is not quite on par with the LP-E6 battery (that I had in my Canon 6D) but then again, that battery was a beast.
FYI the A7 III does not come with an actual battery charger - instead you get a USB cable so you can charge the battery in-camera. Handy to some extent, this quickly got old for two reasons: 1) I couldn't use the camera while charging my spare battery. 2) Despite the sturdy build of the A7 III, the plastic hatches that cover the ports seems pretty flimsy to be honest. This means I don't want to open and close them more often than absolutely necessary. So instead I bought a Newmowa dual battery charger ($14 on Amazon, also sold under the name Kingma) which had gotten good reviews. This will charge two batteries simultaneously with LED indicator lights to show you charging/full status. So far, I've had no issues with it. It's light and incredibly compact so it's perfect to travel with. Sony's own battery charger is too expensive ($90) and bulky in my opinion.
Bottom line: the battery life of the third generation Sony Alpha cameras should no longer be the reason for you to hesitate trying them.
Silent shooting
I remember that some of my previous DSLR's had a "silent" shooting mode. Sure, it was less noisy than the normal shutter sound, but silent it was not. Mirrorless cameras have the ability to shoot 100% actually silent - as there is no clattering mirror when you take the shot. Even with that knowledge beforehand, I still marveled the first (many) times I fired off 10 fps without my surroundings having a clue. I cannot begin to describe how handy this feature is; for street and candid photography, when shooting in situations like weddings where you want to disturb the moment as little as possible, and so on.
The silent shutter mode has its limitations however - it's not ideal for fast moving subjects due to rolling shutter effect. Make sure to switch back to normal shutter mode if you're shooting sports, animals, vehicles in motion, etc.
Additionally some LED light sources may cause "banding" - slightly darker broad bands across your picture - due to the frequency of the light emitted by the light source. YMMV. This can be a nuisance as there inevitably will be situations where you want to shoot silently in these light conditions, but the only solution will be to use the normal shutter mode.
Button customisation
I've constantly heard people online complaining about the deep Sony menu system. And yes, it is quite extensive - perhaps due to the array of features and settings. That being said, there are plenty of good online tutorials that painstakingly go through every single menu item, describing what each one does and their recommended settings (for people like me who never read the user manual). I've watched this and this. It's an hour well spent - as getting your custom functions and buttons set up will make the camera much more intuitive for you.