Is "this last year" proper English?

I came across a very similar phase while reading Pride and Prejudice.

“Mr. Bennet, how can you abuse you own children in such a way? You take delight in vexing me. You have no compassion for my poor nerves.”

“You mistake me, my dear. I have a high respect for your nerves. They are my old friends. I have heard you mention them with consideration these last twenty years at least.”

No, I do not think that "this last year" is proper English, but Buttigieg may have made a small mistake and typed "last" instead of "past."

I've heard this last year before, and the phrase will be understood as "in the past twelve months".

That said, for some reason I can't articulate, this last year has always sounded inferior to these other options:

a. this past year

b. in the past/last year

Is “this last year” proper English?

Yes, it means "in the 12 months prior to today"

This contrasts with "last year" which [currently, and in most contexts,] refers to the whole of 2019.

Have a look at the examples given in Google Ngram Viewer.