Building on the earlier suggestion, I would suggest being a bit careful before dropping that much cash on the GM II. It is an amazing lens, dont get me wrong, but for a lot of video work you might want to consider if the price tag is really justified for your specific projects. I always worry about overspending on one piece of glass and then having no budget left for lighting or audio which are just as important.

• Sony FE 70-200mm f/4 Macro G OSS II: Honestly this might be the safer bet for most people. It is native so the AF is still incredible and it is way lighter. Since the a7S III is a low light beast, losing one stop of light isnt usually a dealbreaker.
• Tamron 70-180mm f/2.8 Di III VC VXD G2: If you absolutely need f/2.8 but want to be smart with your money, this is a solid alternative. The autofocus is surprisingly snappy for a third-party lens. Just make sure to think about whether you really need that extreme tracking performance or if a slightly more modest setup would do the trick... it is easy to get caught up in the hype tho.

Ngl I spent way too long trying to save a buck with third party options before finally realizing that for video, the native stuff just hits different. I was shooting a wedding last month and the way the newer Sony glass tracks eyes while zooming is honestly a game changer compared to what I was used to. The tech they put in their own lenses usually translates to way smoother focus pulls and less hunting. Basically if you are doing professional video work where you cant afford to lose focus, just go with Sony. You cant go wrong with any of their newer native glass because the integration with the a7S III sensor is just seamless. I noticed that third party stuff tends to stutter a bit more when you are pushed to 120fps, whereas the native glass stays locked on. Its definitely more about the internal motors and how they talk to the camera body than just raw speed.

The Sony FE 70-200mm f/2.8 GM OSS II lens offers exceptional autofocus performance for video on the a7S III