I think it's been replaced by "that", as in:
"Upon the submission of the cause the appellant made a motion to amend its assignments of error. That motion is now granted."
"Upon the submission of the cause the appellant made a motion to amend its assignments of error. That motion is now granted."
Is there some formal ambiguity in the two-sentence version which the one-sentence version does not have?
I have often found the writings of legal professionals especially compelling when I've encountered them informally in the wild (newspapers, articles etc) and would like to replicate it myself.
> The local cafe that my dad loves has a lot of lunch options.
> The local cafe, which my dad loves, has a lot of lunch options.
But British English generally uses "which" for both:
> The local cafe which my dad loves has a lot of lunch options.
The "cannot function as a parenthetical" is essentially what a restrictive clause is, although of course the person you're replying to broke things into two sentences.
*Upon the submission of the cause the appellant made a motion (to amend its assignments of error) that motion is now granted.
The current ungrammaticality of the original example given in OP is due to the presence of "motion" within the wh-phrase (c.f., "Which motion is now granted?"), which does not have an equivalent construct for restrictive clauses using "that".