It looks like plymouth's threshold for scale 200% is 192 DPI. And mutter's threshold is 135 DPI. Since my laptop with the bug is 201 DPI (or 198.6 according to the code) then it should be scale 200% for both mutter and plymouth. But a fudge factor was introduced in mutter 44.0 (https://gitlab.gnome.org/GNOME/mutter/-/merge_requests/2880) which means it doesn't actually honour 135 as the target DPI despite the source code saying it does.
It looks like plymouth's threshold for scale 200% is 192 DPI. And mutter's threshold is 135 DPI. Since my laptop with the bug is 201 DPI (or 198.6 according to the code) then it should be scale 200% for both mutter and plymouth. But a fudge factor was introduced in mutter 44.0 (https:/ /gitlab. gnome.org/ GNOME/mutter/ -/merge_ requests/ 2880) which means it doesn't actually honour 135 as the target DPI despite the source code saying it does.