Dear Arlo,
In his Sanskrit introduction to the first volume of the Nirnayasagara edition of Patañjali's Vyākaraṇa-Mahābhāṣya (1917, p. 16, fn 5), the editor Shivadatta Kuddala says that this verse is from Parāśara-Upapurāṇa. The same source is given for the traditional definitions of Sūtra and Vārttika. (Kuddāla, Intro, p. 12 and 14). For the definition of Sūtra, Kuddāla also refers to Viṣṇūdharmottara (ibid, p. 12). On p. 11 of his Introduction, Kuddāla quotes the following verse from Parāśara-Upapurāṇa:
pāṇinīyaṃ mahāśāstraṃ padasādhutvalakṣaṇam /
sarvopakārakaṃ grāhyaṃ kṛtsnaṃ tyājyaṃ na kiṃcana //
From this it appears that there is a section in the Parāśara-Upapurāṇa dealing with Pāṇini, and the definitions of Sūtra, Vārttika and Bhāṣya likely appear in that section.
I don't have a copy of Parāśara-Upapurāṇa with me at hand, but that is one possible source to check. Hope this helps. Best,
Madhav Deshpande