I don’t think it would matter that much since a desktop at 3k is very similar on modern hardware to a desktop at 1080.
But I’d be interested in someone who had the hardware to test this. Right now I use my laptop for school work, and in trying to squeeze every ounce of battery life I was running my display at 45hz instead of 60hz. I had a free day during the summer so I charged it up, ran a YouTube video on repeat and timed the battery life, then changed the display frequency and it was like a 2 minute difference. I also tried it while running a second 1080p monitor through hdmi and the difference was something like 10 minutes. Like, so small a difference or didn’t matter.
I don’t have the data sheet anymore so these numbers are anecdotal etc etc YMMV. The biggest change for me was buying a 65w PD battery bank and keeping that charged in my bag.
If you’re a sewer, you can probably convert some fabric and a cloths hanger into something similar.