Bird in flight is a tough one. Never tried it.
I think that is a very important point. I can only compare Lumix telezooms with Olympus telezooms on Lumix and Olympus bodies for sports photography. The body did not matter at all. It was the lens.
The Olympus lenses were always faster, snappier than the Lumix lenses. Oly 40-250/2.8 vs. Leica 50-200/4.0, 35-100/2.8 Mkiii, all on G9 (only DFD!) and EM1.3.
I see similar differences now with my S5ii snd the Sigma 100-400 DG DN and Lumix 70-300. Both sre great lenses and both have a fast AF. But not as fast as the old Oly 40-150/2.8 Pro for MFT.
The Sigma 100-400 is "only" a contemporary lens. Not a sport lens. The AF is accordingly as expected and nothing to complain about.
The Oly 40-150/2.8 Pro was designed for sports and wildlife. That shows. There are longer lenses from Oly and Panasonic in MFT, but their AF is slower than the 40-150/2.8.
Atm I do not see any sport telezoom in the L-Mount line up except the new Sigma 300-600mm.
The Sigma 50-600, 500, and 300-600 all have updated, faster AF motors. Presumably if Panasonic ever gets around to releasing their telezoom that has been on the roadmap for years, it will have fast AF as well. At least, we can hope. Sigma really ought to release updated versions of the 100-400 & 150-600 with the new motors. Now that we have the S1RII & S1II, perhaps they will.
Now, should Panasonic release some fast (and expensive) tele primes to compete with Nikon et al? That doesn't make sense to me until they release a true professional grade sports cam (hires fully stacked sensor, large buffer, a competitive AF system, etc). Of course, the Sigma CEO said he would like to release such a camera, but that was far from a commitment.
You do have to wonder if it makes sense for Panasonic to do battle with Canon/Sony/Nikon at that level. Perhaps it will if they manage to bring newer, younger shooters into L-mount, and then want to give them an eventual path to pro-level bodies. But as I understand it, most existing professionals don't switch systems very often, let alone bodies. So while the upgrade path might make sense eventually, I'm not sure just going for it right now and doing a head-to-head competition in that sub-market makes sense.
Having said all that, if Panasonic made a Z8 competitor in a few years, I could see myself buying it, presuming I end up enjoying sports/wildlife sufficiently.