I have a Canon EOS R6, EF600mm F/4L USM (non-IS, so I believe the initial 1980s version, very heavy lens), using a tripod w/Wimberley WH-200 Gimbal Head. Lens is of course connected using the EF mount adapter.
I am able to get sharp photos, but all I've checked have F7 through F11, and shutter speed is 1/2000+ (the two I spot-checked are 1/3200). The attached pic of ducks was F7.1, 1/3200, ISO 8000, no extender.
One thing, depth of field w/this 600mm is immensely shallow, and even more so with the teleconverter. If subject eyes are sharp, the ground (or even parts of the subject) immediately behind and in front is blurry at F7 through F11. F6.3 (your pic) is likely more shallow... though you have a newer lens so maybe not the same experience.
I've captured some good photos and video with this lens but its not like all photos are handed to me on a silver platter.
Your lens with IS should allow for flexibility. I have heard of IS getting in the way for some action shots but the examples you posted were not seeming action shots. Light seems relatively low as well. Not being a professional, I would offer my vote re what others pointed out, your shutter speed sounds slow even for slight movement, and depth of field at F6.3 might produce blurry subjects if eyes are not focus point.
I get many more fuzzy shots than tack sharp shots... I must really ensure high shutter, sturdy mounting... in my case, I worry about wind since I do not have a top tripod... a good tripod but a little wobbly with strong wind when at max extension.
Below/attached you can see center duck is sharp, behind and in front are soft. Not saying it's a great photo but it makes the point, these ducks are close, I'm at a distance from the water, F7.1, but just behind and in front is soft.
