while we still havent really reached good mobile budget laptops with good battery
an LG gram (22h battery and just 1kg - at least the 16inch I think) would be a dream
but still around 800€ used

I think if you want to go budget a mac early 2015 might be an idea. Less than 200 dollars :D

Link
I am not sure about battery replacement stuff

I bought a ThinkPad X1 a couple of years ago when I was in China. Maybe around 900 dollars (new). At that time I didn't have to do much computational work and didn't know remote desktop-ing was a good idea. Hopefully last me 10 years :3

I think the battery duration thing is also partly related to Linux as it cannot properly optimize for long usage. I used to have a double boot on an old ThinkPad Tseries. For basic typing stuff in Latex the battery duration would be greatly in favour of Windows. I think over 30%