All of the recent (4+ years) cameras have a "share to mobile" feature, where the camera acts as an AP, and your phone connects to pull photos from it. You can either pick the photos to transfer on the camera or on the phone, and it works pretty well for posting to social media, or instantly sharing.
I've run the RX100M3/M5 and a7iii off of USB power forever (a full day's worth of being a webcam via HDMI capture). You can get a battery eliminator for the older a7 models -- while it does require additional hardware and hassle, they do work, and can run off of USB.
The a7iii _finally_ supports some level of geotagging by using the GPS in your phone, and using a BLE connection to get location. It's not as good as a built in GPS, but it's better than recording a track log and syncing later.