Prelimineries
What you describe in the second part of your post is close to what Kant himself states at the end of the introduction of the Critique of the Power of Judgement, 5:198, in form of a table:
| All the faculties of the mind |
Faculty of cognition |
A priori principles |
Application to |
| Faculty of cognition |
Understanding |
Lawfulness |
Nature |
| Feeling of pleasure and displeasure |
Power of judgment |
Purposiveness |
Art |
| Faculty of desire |
Reason |
Final end |
Freedom |
Here, the rows correspond to the first, third, and second critique respectively.
In the table, we have the faculties of the mind, which Deleuze calls "higher faculties", the active faculty which does give the a priori rules for it ("legislates it"), what the underlying principle to all rules is, and which objects they apply to.
What is less clear is how this corresponds to the 2-dimensional analysis above. He does write the following with regards to the second (not "higher") sense of faculty (quotes from Deleuze, Kant's Critical Philosophy, 1985 edition):
We must distinguish between, on one hand, intuitive sensibility as a faculty of reception, and, on the other, the active faculties as sources of real representations. Taken in its activity, synthesis refers back to imagination; in its unity, to understanding; and in its totality, to reason. (pp. 8-9)
But since only the latter three are active faculties1, it is only them who can give re- presentations:
The important thing in representation is the prefix: re -presentation implies an active taking up of that which is presented; hence an activity and a unity distinct from the passivity and diversity which characterize sensibility as such (p.8)
And, thus, we only have to care for these:
In short: to each faculty in the first sense of the word (faculty of knowledge,
faculty of desire, feeling of pleasure or pain) there must correspond a certain relationship between faculties in the second sense of the word (imagination, understanding, reason). (p.10)
Ignoring the details, I think that up to that point, the analysis is more or less "obviously" correct insofar as it bears semblance to Kant's own table, even though Kant does write about the "power of judgement" as a separate faculty in the table. What I cannot do here is discuss all the literature on what the power of judgement is supposed to be, whether it is a faculty in its own right, etc., since that is a Kantian field of study in itself. It may suffice for the moment to say that there is some reason to assume that what Kant calls reflective judgements are dependent on productive, i.e. "self-active (as the authoress of voluntary forms of possible intuitions)" (5:240), imagination. So let me say something on "whether Deleuze's analysis is still considered as valid nowadays by Kant scholars".
Actual answer
Now, the broader question is a bit tricky to answer. I think there are three points to consider if one wants to be fair to Deleuze:
Firstly, Deleuze does not assert that the objects of the respective kinds are given by a single active faculty. For the higher faculties of cognition and desire, he argues why there is a single active faculty taking the lead, as it were, but also how they necessarily are in interplay to produce objects of experience since they cannot do so by themselves. As of the third one, he argues with Kant why there is an active, open-ended interplay where there is no lead but only some kind of harmony between the faculties. And whether it is clear-cut that lawfulness is a concept (given by understanding), purposiveness is a schema (given by imagination), and the final end an idea (given by reason) may be questioned at least for the former two. So it is not as easy as it may come across from your description, and I would say that's not what Deleuze wanted to say as well, but it certainly does not add up as neatly considering what Kant himself wrote. Maybe it rather tries to invoke what Kant should have done.
Secondly, the interplay and demarcation of the faculties are subject to contempt and discussion up to this day. Especially the role of imagination as a separate active (rather: cognitive) faculty is problematic since Kant seems to change views from the first to the third critique (there are arguments for why he doesn't as well). Thus, assigning a clear role of giving schemata only is simplifying at best. Imagination clearly is described as being able to produce representations of actual objects at some points, we have to differentiate between reproductive and productive imagination, and Kant does write that even the latter is not spontaneous in the sense of adding any matter of its own, but at the maximum in its ability to combine previously sensed content in new ways, ie. it can only rearrange intuition (Anthropology, §28). Does this still mean it gives schemata only, even though it seems to deliver representations from memory as well? That highly depends on the understanding of what schemata actually are. This whole complex in itself is still far from being settled within the literature. If you want to go deeper into this, Imagination in Kant's Critical Philosophy, edited by Michael L. Thompson, may be of interest to you. It does not
Thirdly, Deleuze is broadly ignored by all analytic and most prominent continental Kantians these days as far as I am aware. A cursory search in my electronic library of secondary literature on Kant did give no hits for this work by Deleuze and it includes many texts written by the usual contemporary suspects (Ameriks, Allison, Guyer, Timmermann, Förster, and others). There obviously is some attention to this text still, since Google Scholar does give 153 citations since 2017 alone. Most of these are on Deleuze and postmodernism, though, and not written by more or less renowned Kant scholars.
A possible candidate
What seems to come closest is the recent Kant: Anthropology, Imagination, and Freedom by John Rundell, which seems to take up the idea of imagination as delivering specifically human schemata and also seems to be an interesting book in its own right. So I suspect Rundell does to some extend affirmatively refer to Deleuze. I did not have the pleasure to study the book myself yet, though. Other works referring to this text are by authors as various as Kukla, Makkreel, and Bennett.
Concluding remarks
While the review linked by @Conifold does attest some relevance and the text certainly does offer some insights and interesting takes on the subject matter which are thought-provoking, I would argue that it is, in fact, and with good reason, largely dismissed by contemporary Kant scholars as an accurate analysis as a whole since it is simply inaccurate or painting with a broad brush at times. The conceptual demarcations are not refined enough and stand at odds with explicit definitions given by Kant throughout his work, especially the often-dismissed Anthropology.
1 Strictly speaking, passive or receptive abilities are not faculties in the Kantian sense, see Anthropology, 7:140: "In regard to the state of its representations, my mind is either active and exhibits a faculty (facultas), or it is passive and consists in receptivity (receptivas)"
