Padma purana classifies puranas according to gunas, but is this classification mentioned by Shankara or Ramanuja?
Yes, both Adi Shankaracharya and Ramanujacharya believed in it. Here is what Adi Shankaracharya says in verse 371 of the Sarva Vedanta Siddhanta Sara:
By listening to Sattvic Puranas, by eating Sattvic food, and by serving Sadhus, one increases Sattva Guna.
And here is what Ramanujacharya says in this section of the Sri Bhashyaa:
And as to the third point, Hiranyagarbha himself is only an individual soul, and hence liable to be overpowered by the inferior gunas, i.e. passion and darkness; and hence the Yoga-smriti is founded on error, no less than the Purânas, promulgated by him, which are founded on ragas and tamas.
"Thus the (Vishnu-Purana) exhibits itself as meant solely for the declaration of the determinate identity of the supreme Brahman. 158. All other Puranas with other aims must be interpreted consistently with this Purana.
That they have other aims is discerned in the manner of their commencement. Whatever is found in them, altogether inconsistent with this Purana must be set aside as being of the nature of tamas"
from the above quote from the vedartha sangraha it looks like ramanuja regarded vishnu purana as purely sattvik and other puranas that have the same aim as the VP as Sattvik also. Puranas that do not share the aim of the VP would be judged by content not the whole purana: any content in such Puranas in disagreement with the VP would be tamasic, according to him.