Here it is (almost) mid September (2025) and the problem has not reoccurred (i.e. my Sony a7iii Camera is still remembering the date & time when turned-on). A few days recharging the internal 'RTC' (real time clock) battery seems to be adequate.

NB: I will NOT be responsible for any broken/unusable teleconverters. Also, I just want to preface this by saying that I am NOT a Sony shooter; I am personally a Canon shooter so there is no way that I can verify this myself.   Sony's restriction of 3rd party glass using teleconverters is pretty well known. I had a friend who uses Sony and shoots wildlife with me, and he was kinda jealous of Canon and Nikon for having affordable supertelephoto prime lenses available via EF to RF or F to Z adapters. Sure, you could always adapt EF or F glass to E mount, but the autofocusing performance is always lacking.   This was until the release of the Sigma 500mm f5.6 for E mount. However, my friend is still hesitant to get the lens due to the inability of having teleconverters. While researching for him for alternative solutions, I stumbled upon a comment on a video on the Chinese video platform Bilibili saying that there is actually a way to have the Sigma 500mm f5.6 with the 1.4x teleconverter. I messaged this commentator (whom I won't disclose) and this is the method that he entailed:   One could open up the Sony teldconverter, rewire the contacts, so that the contacts on the male side connects directly to the female side, bypassing the chip inside the teleconverter completely, and thus the camera body would not know that a teleconverter is mounted with a 3rd party lens, and the autofocus should work. It should be a fairly easy job, only requiring some soldering skills.   Is anyone willing to verify this? I understand that the teleconverter is still quite an expensive piece of kit, so please don't try this if you're not confident with your soldering skills, or you care about the water resistance performance of your teleconverter, etc. Cheers

I use the 24-105 on an A7 IV and an A1, and never feel any vibration of any kind when turning the camera on.