Moving to a larger (higher resolution) monitor

I have LR Classic set to create standard previews that are 2048 pixels (since my current display is 1920x1080) and Adobe recommends that you create previews that are slightly larger than your actual resolution for them to render correctly (I guess, at least how I interpret the recommendation).

Anyway, if I move to a higher-res monitor, like a 4k monitor, do I need to set the Standard Preview size to say 2880 pixels and rebuild all of them again, or will LR do this automatically when I access the files?

(I used to have the Standard Preview set to Auto, which is 1920 by default but have since changed this after reading the Lightroom optimization recommendations from Adobe).