https://drafts.csswg.org/css-cascade-4/#legacy-shorthand means that for:
<div style="page-break-after: var(--a)"></div>
The following happens:
div.style.cssText == "break-after:;"
It's a bit unfortunate, but maybe it's ok, given this is a more general issue (#2515), and these shorthands are supposed to be legacy anyway. We could fix legacy shorthands by special-casing them and saying that they serialize in this case, but that's not necessarily great, and certainly propagates the weirdness a bit more in the implementation.