The text-underline-position property is in CR spec.
Quick test indicates:
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Didn't know this was a thing, cool!
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I just found out about this, and am having trouble finding proper browser support information. MDN's documentation lists many browser/property combinations as "unknown". It would be really helpful to have this in caniuse.
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Webkit/Safari 12.1 now supports text-underline-offset and text-decoration-thickness.
Description:
The text-underline-offset allows for placing an underline at a specific location below the baseline. The text-decoration-thickness property specifies the thickness using a length value — a number followed by a unit (e.g. 1px or 0.5em). Rather than using absolute lengths, using em units in both of these properties is preferable here so that the line thickness and offset scales with the font size. You can also specify from-font to both of these properties which will pull the relevant metric from the used font file itself.
Documentation:
https://webkit.org/blog/8718/new-webkit-features-in-safari-12-1/
We should add both text-decoration-thickness and text-underline-offset. As stated above, both are now supported in Safari 12.1+. And we are implementing them in Firefox.
Here is the current support data according to MDN

Ah, text-underline-position and text-underline-offset are two different things. I'll go open a different issue for the latter.
This feature will be shipped with Chrome 87.