What would be good textbooks at the graduate level that deal with Labor Economics and Labor-Macro (As in, Equilibrium Unemployment Theory, Shimer Puzzle etc)?
There's also Labor Economics by Pierre Cahuc, Stéphane Carcillo, and André Zylberberg. It's a broader labor econ book, but The "Unemployment and Inequality" fourth of the book covers these topics. I have not seen the second edition, but I expect that they did not alter that part for the worse.
To get us started, I will suggest
Pissarides: Equilibirum Unemployment Theory
Which deals with his Search&matching Equilibrium model of Labor Markets, and various extensions.
I'm not sure if it's a good book, the author at least is very known in the macro community, but if you want a book on the New-Keynesian perspective on unemployment:
Jordí Galí's He tends to leave many details outside the book. You might like it.
To add another book,
deals with the extent of which the RBC model and the Mortensen-Pissarides model can deal with the Shimer puzzle. He goes through many extensions and concludes that rigid wages are an exciting future research avenue.
So the following is not a textbook, but it is a long and informative chapter on search-and-matching models from two experts in labor-macro:
Rogerson and Shimer, 2010: https://ideas.repec.org/p/nbr/nberwo/15901.html
The notes by Acemoglu are quite useful too.
There are whole sections on Labor Economics, but also a lot of scattered material throughout the rest of the topics, particularly related with technological change and growth. That is particularly relevant with the Macro-Labour component of your question.
To single out one relevant topic which is not in the references in other answers, consider these notes on "Labor coercion" (slavery, serfdom).