It 100% solved the problem for me. With Increase Contrast on I saw lyrics in dark mode but NOT in light mode. With Increase Contrast off, I see lyrics in both modes.
This is a bug on Apple's side, there is no "solution" to this problem other than Apple fixing the bug. For some people (such as myself), turning Increase resolution OFF fixes the issue. For others (such as you, apparently) it does not fix the issue. And for many others this isn't an issue at all, lyrics show up regardless of the setting for Increase Contrast or the setting for light/dark mode.
This is an Apple problem, not a settings problem