Late to the party but +1 to what was said earlier about nits. Seriously, if youre shooting outside with the Sony a7S III, anything under 1000 nits is basically a paperweight. I mean, i spent way too much on high-end gear before realizing i could save a ton of cash. Unfortunately, i had issues with some expensive recording monitors overheating during long 4K 60p sets which was not as good as expected for the price. Tip: Try the PortKeys PT5 II 5 Inch Camera Monitor if you just need focus assist and LUTs. It is way more budget-friendly, usually around $125. But honestly, my biggest caution is to spend the savings on a legit Kondor Blue Braided HDMI to HDMI 2.0 Cable. I have seen too many budget setups fail because of cheap cables dropping the signal at 4K 60p... total nightmare. If you really need that outdoor brightness, the Feelworld FW279 7 Inch Ultra Bright 2200nit is a decent alternative for under $250, though the build quality is kinda meh. Anyway, just be careful with the strain on your HDMI port!!!

Ok so, i totally get the struggle cuz the a7s III screen is basically microscopic when you are trying to nail focus at f/1.2! Honestly, if you are doing outdoor shoots, you highkey need to prioritize the Nit count or you wont see anything but your own reflection. I have been through three different setups for this specific camera, so here is the technical breakdown. In my experience, these are the best options for what you are looking for:

• Atomos Ninja Ultra 5.2-inch 4K HDMI Touchscreen Recording Monitor is basically the industry standard for a reason. Even though it is 1000 nits (which is okay, maybe not amazing in direct noon sun without a hood), the OS is super snappy. Since you are shooting 4K 60p, the processing power in the Ultra handles the HDMI handshake lag way better than the older Ninja V. Plus, you get ProRes RAW support which is amazing for the a7s III dynamic range.
• PortKeys BM5WR 5.5-inch 2200-nit HDMI/SDI Touchscreen Monitor is actually my top pick for pure visibility. It hits 2200 nits which is seriously bright. The color accuracy is decent, but the killer feature is the wireless camera control. You can actually change ur camera settings like ISO or shutter right from the monitor interface. It handles 3D LUTs via USB and the latency is almost zero even at high frame rates.
• SmallHD Ultra 5 High-Brightness Touchscreen Monitor is the one if you are a total technical nerd for color. Their PageOS 5 software is fantastic for technical analysis like EL Zone or waveforms. It is 3000 nits, which is insane, but it is pricey. Basically, if you wanna record externally, go Atomos. If you just need to see ur focus in the sun, go PortKeys. Just make sure you get a high-quality Zilr 4K High Speed HDMI Cable with Ethernet to keep the signal clean! gl!