As for the water left over after an animal has drunk:

Under item 3 he says: “On the authority of Jābir (may Allah be pleased with him), the Prophet ﷺ was asked, ‘May we perform wuḍūʾ with the water left by asses?’ He replied, ‘Yes, and with what all beasts of prey leave behind as well.’ The report was transmitted by al-Shāfiʿī, al-Dāraquṭnī, and al-Bayhaqī, who remarked, ‘It has several chains; when they are combined they become strong.’”

I say: This ḥadith is weak, exactly as al-Nawawī stated in al-Majmūʿ, 1/173. He went on to say, “I have cited this ḥadith—despite its weakness—because it is well known in the manuals of our colleagues, and some of them may have relied on it, so I have pointed that out.” May Allah reward him well.

As for al-Bayhaqī’s comment just quoted, a look at his documentation of the report in al-Sunan al-Kubrā, 1/249–255, shows that he is referring to its chains that revolve around Dāwud ibn al-Ḥuṣayn, from his father, from Jābir. All of those isnāds are weak, as al-Bayhaqī himself intimates, for they all rest on that very transmission line. Although Dāwud is listed by al-Bukhārī and Muslim, several critics still judged him weak, and his father al-Ḥuṣayn is graded “soft” in ḥadith according to al-Taqrīb. Some unreliable transmitters even omitted the father altogether, leaving the report as Dāwud narrating directly from Jābir; this removes the weakness associated with the father, but Dāwud never met Jābir, so the report becomes disconnected.

Beyond its chain, the text itself is objectionable because it clashes with the ḥadith of the two qullahs. That latter ḥadith was delivered in answer to someone who asked about water affected by domestic animals and wild beasts, and the Prophet ﷺ said, “If the water reaches two qullahs it does not carry impurity,” and in another wording, “it is not rendered impure.” Ibn al-Turkumanī observed in al-Jawhar al-Naqī, 1/250: “The outward sense of this indicates that the water left behind by beasts of prey is impure; otherwise, the condition of ‘two qullahs’ would be pointless.”