Not really relevant: power requirements would affect battery size much more than charging port size. And USB-C supports much greater power transport than the old dock connector.

Given that an iPod nano only lasted a few hours on a charge and most smartwatches can last multiple days, I'm pretty sure that's not so. Even if they had apples-to-apples identical functionality I think a modern device would consume less power simply due to current chips being more power efficient via using smaller dies and lithography processes.

Plus, an iPod has to crank its weedy little processor full time as long as it's playing music. Your smartwatch pretty much only has to do anything when an external stimulus wakes it up, be that pressing a button or tapping its screen or receiving an alert or whatever. I've developed software for some of the Garmin models myself and I can tell you that the power consumption and processing time limitations imposed by the system are extremely stringent. The majority of the time even in a second-by-second basis your watch is completely idle, specifically to consume as little power as possible and conserve the battery.