Went to Sony land. More or less satisfied. Any system has its pros and cons. A7SIII does many things sufficiently to make money with. Also went with FX6 for a bigger camera but I only use it on sticks. Otherwise I use a gimbal with the A7SIII. Depending on your style the IBIS may work - it's decent for static shots, but for walking shots it's not so great unless you're using a gimbal. On the other hand if you can live with the current process for the gyro stabilization, you can use that as well.
I much prefer what I can get out of the Sony color wise. I use the usual slog3 except I typically use the Phantom luts, although I must say I don't like the current version and still use the older version. I will say that the NR is very heavy handed in low light. Since COVID times I haven't done any events so I haven't explored that area myself, but I know the A7III I used was streets ahead of the GH5 so I think I'll be fine.
I really hated the color and DR from my GH5 even if the weight and IBIS were good. Most GH5 footage seems to be from either (no offense) wannabe filmmakers where the grade always looks like something is wrong with the contrast curve, or from videographers who don't have an eye for color. There's a few people who can make it sing and I definitely couldn't, but maybe you can.
Otherwise the S5 low light looked very very good color wise, but there's the trash Panasonic AF and the lens selection... Manual focus during fast paced weddings - good luck for the average person.