ilia's,
In addition to what Kevin stated, is your A7SIII footage encoded in XAVC-S or XAVC-Si? If yes to either, then you will not have hardware-accelerated decoding at all regardless of which CPU or GPU you have. Hence, you will suffer from choppy playback regardless of CPU or GPU.
If on the other hand your footage is in XAVC-HS, then your system does not support hardware decoding at all. For Windows, only systems powered by an 11th-Gen or newer Intel Core I-series CPU that have integrated Intel on-CPU graphics both present and enabled support 4:2:2 HEVC at all for hardware decoding. All other PCs including yours support only 4:2:0 for hardware decoding, and in the case of H.264 only 8-bit.
And though Adobe chose not to support 4:4:4 hardware decoding for HEVC (as newer Nvidia GPUs support), the 4:2:0 restriction is dictated by the discrete GPU manufacturers. In other words, for HEVC your RTX 3060 Ti supports 4:2:0 or 4:4:4 - but oddly not 4:2:2 - for hardware decoding.