Any bodies competitive with Sony c-af or eye-af?

Do you have problems getting enough keepers with the G7? I have very good success with my GM5 and GX80 using AFF and the smallest focus area, which I put on the eyes of my subjects. Panasonic's CDAF is not only very fast, but also extremely precise and sensitive. That is what I need for getting a high keeper rate when shooting children, including indoors.

The focusing system in my A7 III is a bit of a step back in this regard, as the smallest area fails to acquire focus in AFC way too often and one is thus forced to use the larger "expand flexible spot", which is less precise as it is too large in some situations (and AFS is pretty slow). Even then, the A7III slows down indoors much more than Panasonic, especially when one has to stop down (focus is tracked stopped down in AFC, in contrast to wide open with Panasonic).

The A7III has much better eye AF than my Panasonic cameras. The GM5 is ok for still subjects, the GX80 for slightly moving ones, but the A7 III identifies people much more reliably and tracks the eye with way more confidence. However, it still fails to identify the eye/face sometimes (so one should have a plan B) and it has a tendency to focus on whatever is in the front in the focusing area (eyebrows or glasses). Glasses are a big problem with the A7III in general, as the camera fails to identify faces with glasses around half of the time and even if it succeeds, it most often focuses on the glasses. Using the "expand flexible spot" instead of eye AF is often not much better, as the area is too big to selectively focus on the eyes behind the glasses.

The PDAF system in the A7 III is better with fast moving subjects, where a large focusing area is necessary, e.g. in sports or BIF. It focuses on the subject in the foreground much more reliably, while Panasonic's CDAF might go for the background, especially if it is busy. It's not unusable, but the keeper rate goes down substantially if one is not able to use a small focusing area, which fits the subject entirely. However, shooting portraits of children is not in this category, in my opinion.

The A7III has a major advantage with AF in video, which is slow and unreliable with Panasonic. If you want to film moving children then yes, the A7 III (or a similar camera with well working PDAF) is a very reasonable upgrade.