If 2% of the battery is 2% of 3000mAh (which is probably a generous over-estimate of the phone's capacity), that means the phone pulls ~60mA.
You can buy a 60,000 mAh battery (or build one) for about $50, which would buy this device 10,000 hours, or round it down and call it 1 year.
It uses solar power, right? So I think it was built with that in mind. charge during the day and run until it loses power at night
How big are 60k mAh safe batteries?
I know eBikes are a massive step up from laptop batteries (seemingly better for the density too somehow?)
https://www.amazon.com/dp/B0CZJDVDLC
This little no-name 185Wh battery pack is $40 right now with the 50% coupon code and would probably work great. (I picked one up recently for another project and it actually does deliver as advertised performance.)
For another use case, I experienced that the phone battery starts swelling after few months. It was an indoor setup and I had removed the phone backcover to avoid overheating.
60,000 divided by 60 is 1000, not 10,000. So only about a month, still a lot of time!
The phone has 4,000mAh, too.