IBM and Lenovo ThinkPad laptop enthusiasts!
What will your main use of the laptop be?
The OLED with 200% display scaling will make it 1440x900, which is a good resolution for a 13". That's not a good resolution for watching videos since it would require non integer scaling for 1080p or 4k content.
The IPS would be great for video, but 1920x1200 will make text rather small on a 13" screen and 200% scaling would make the resolution too low to be usable.
Probably mostly writing and coding
The OLED would work well for that as long as you are careful to avoid burn in. You can extend battery life by using a dark theme, but I don't know if that will make up for the extra power consumption from the higher resolution though.
Thanks. Looking at Notebookcheck reports it seems that in idle OLED uses twice as much power (5W vs 2.5W). For normal browsing experience it's almost nothing but for light terminal usage it will make a difference in battery life.
OLED screen indeed sounds to be a pleasure to the eyes but that 10h+ battery life is equally tempting.
Is OLED burn-in still a thing? Most UIs use some kind of a permanent dock, taskbar or a bar of some sorts
OLED displays have gotten much better, but they still get burn in. There are ways to minimize it like not turning up the brightness higher than needed, setting a short display timeout, setting the task bar to auto hide, and frequently changing the wallpaper. No matter what you do, they will not last as long as an LCD, but the battery will probably fail before the OLED display does.
Since Lenovo only gives you the option of 1200p and the 3k OLED I'd personally go with the 3k display. Not because it's better, but because I dislike 1080/1200p more.
I am NOT a fan of OLED displays on laptops, but 1200p is not enough for me IMO. It's in an awkward spot where I non scaled text can be a bit small and I'd want scaling. But (in windows) the next scaling option is 125% which is too big. Plus the 1080p screen Lenovo gives you is typically hit or miss on quality. I'd hope the Z series are better than T series in that regard.
Since you're using linux the 1200p screen might be an advantage because text in text mode won't be microscopic without doubling it's size, and I'm not sure how all desktop environments handle scaling.
Luckily, I handle font scaling, GUI scaling, and in fact, all of it myself.