Most efficient way to synchronize

They say Bluetooth is much more energy efficient than WiFi...
https://www.netguru.com/codestories/bluetooth-vs-wifi-comparison-for-the-iot-solutions#:~:text=of%20these%20solutions.-,Power%20consumption,consume%20less%20power%20than%20WiFi.&text=The%20difference%20is%20rather%20significant,and%20count%20in%20additional%20costs.

The most efficient would be to plug the watch into a computer with Garmin Express so it charges while synchronizing.

But for wireless synchronization, Bluetooth is much more energy efficient than WiFi.

Use WiFi unless you are using notifications and/or weather widget. Just enabling Bluetooth on the watch drops the estimated battery lifetime by 1/4-1/3. WiFi will sync automatically (not sure the exact "automatic" part), but I have had a sync a few minutes after going home after a run. And since WiFi is a periodic task, even if more power hungry than Bluetooth, will make the battery last way longer.

The big power drains on the watch are GPS, backlight (depending on settings), Pulse Ox, map rendering, music and wrist heart rate. If you are looking to maximize battery life, those are the settings you should focus your attention on.

Phone connection is a pretty low drain activity, but it is on continuously, so usage can add up over a week or two. Personally, I use the Battery Saver mode to turn automatically turn off the phone connection each night, and back on in the morning.

If you are syncing then turning the phone connection off, then the power usage is extremely low, and the difference between wifi and Bluetooth is immaterial.

I do wifi and bt. Whatever you do make sure you are good with updating to GC daily. If you wait for lets say a week it can take a while over bt. Wifi faster and Garmin Express even faster.