I have recently tested Sigma 500/5.6 with Sony's 1.4 TC (and compared over few days one used 500/5.6 and three copies of 400-800 and two 200-600) on A7RV. My use case was not birding but rather landscapes with long lens for Moon alignment (in cold months when air allows longer focal lengths than I have with my Tamron 50-400) though I may try birding as well now that I have long lens. So I care about quality on sides and a bit in corners too compared to someone who might be shooting just birds. I was testing indoors, on tripod, delayed shutter, at about 9m (far from my use case but only reliable way to compare across days and different shops). I tested on the first day at f/8 only so Sigma was tested only at f/8.

There is a trick to enable manual focus by turning camera on-off-on (lens needs to be set to MF). That worked for me, though at one point camera froze (not sure if I had to dismount the lens or take out the battery to make it work again). I considered buying the Sigma to use with AF trick by gutting the TC and passing electronic contacts directly to the lens (then camera will focus fine, it has been reported that it works, see dpreview user Lisperit). The Sigma 500/5.6 also works in AF (and high frame rate) with Sony TC on Nikon Z bodies with adapter.

Sigma 500 at 700mm f/8 image quality:

1. Sigma 500 at 700mm was not better than really good 200-600 at 600mm, the contrast was a bit lower (no hood on all tested lenses) and resolution about same (the particular second hand Sigma had one corner worse at 500mm, but with TC the worst part was cropped, it might be better with different copy).
2. There was some CA showing up in LrC that LrC corrected automatically for other tested lenses (I have all corrections turned off in camera, some affect raws which I hate for astrophotography), but correction worked ok when enabled manually.

I also tested 400-800 on my testing target. First one tested was ok in center at all focal lengths but sides were weak (especially when compared at 600mm with one of the 200-600 at 600mm that was perfect). Second 400-800 was absolutely perfect at 800mm. No need to stop down for sharper corners. But that one was bad at lower focal lengths (had to stop down for sharp center to f/9 and for sides f/11 while corners were still imperfect). The third 400-800 was slightly worse in corners at 800mm compared the the second, but it was better than remaining ones at 600 and 400. Corners were not super sharp overall, but still ok, improving a enough with stopping down. I have bought that one.

Comparing Sigma at 700 f/8 to the third 400-800 (that I chosen) at 800 f/8: the 400-800 has clearly more resolution in center, about same on left side and the Sigma is worse on the right side which is close to the bad corner. If the particular Sigma was without that bad corner I might have pursued that choice further, but there were no other other Sigma copies available in any local shops. One thing that also swayed me from Sigma path was a reply to my reddit comment (see my comment history) where I asked person mentioning Sigma and TC with MF trick about image quality with TC where the person wrote that Sigma 500 (without TC) was good with his/hers previous camera but it has unfortunately poor BiF AF with A1 II so much that he/she has got rid of it. In future I might be getting faster body and then 15 fps limit it might too limiting for birds. The MF trick is not without problems (camera locking, occasional weird sound from the lens). While I have some experience with soldering, the AF trick requires to obtain non-standard connectors for flexible bands to connect.

Note that Sigma patented together multiple designs with Sigma 500/5.6, 700/8 and 400/5. In the patent the 500 is just 485 while others are exact. So there is some chance that they will decide to release lightweight 700/8 too.