Re Refurbished: can confirm, Apple refurbished is not an issue.
Re Battery life: Take a look at the image attached, JustJosh youtube channel from the M3 Macbook air review.
73% of 55.6 Whr is like 40.6 Whr left which means it used 15 Whr of battery
75% of 70Whr battery is 52.5Whr. Which means it used 17.5Whr of battery for the same task. So yes it uses more battery to do his netflix 4 hours test at equal brightness, but has a nearly 22% larger battery to compensate. (But this is also the 12c model, if the M2 Pro MBP youre talking about is the 10 core model, battery life will be even better)
Some other things to consider:
Do you plan on connecitng out to external displays a lot? If so the m2 Pro chip is going to be much better. has an HDMI port built in and supports 2 external displays while driving the built in one. M3 Air you get 1 external display support or have to shut the lid to use 2 external, plus you'll need an HDMI adapter. (but you might already have one)
yes the M3 is going to be faster for lightweight tasks thanks to the improved single core performance. Will you really notice it? No, not unless you have both machines side by side for comparisons sake.
the MBP is heavier like you said, but you get more ports, a better screen, larger battery, and a better GPU/multicore performance chip. Though the more performance here maybe isn't applied to your use case that much. If you're streaming GeForce Now for extended sessions the fans may come in handy. The more performance becomes more useful if you end up playing games on your Mac in the future.
If you watch a lot of youtube/netflix the M3 chip has AV1 HW decode which both those sites are going to be using more moving forward so in the long term it may benefit more from that. But no way to know for sure without tests comparing them.
That 4K HDR content from youtube and netflix is going to look much better on the MBP display. I have an M1 Pro 14 inch and it's incredible.
You're buying this for school, what is your major going to be? If its going to involve engineering/coding/media editing then the Pro is probably better.
Now I realize I'm not giving you good advice in terms of "go buy this" but you should decide what matters to you right now, and in the long run.