How to introduce search and matching in NK (or RBC)

I’m looking for introductory bibliography regarding DSGE (RBC or NK baseline) models with search and matching dynamics in the labor market that allows for employment/unemployment explicit modelling.

In the other hand, to my best knowledge Lagrange method for optimization is no longer valid in this kind of problems, and one is forced to use Bellman equation and related theorems for optimality conditions, therefore I’d be thankful if you could provide me some introductory literature, I’ve already checked very superficially Ljungqvist and Sargent’s (2012) “Recursive Macroeconomic Theory”, nevertheless I’m not aware if this book is suitable for self-taught introduction, so I’d like to know if it’s worth to do that with this book.

Last but not least, will equilibrium and optimality conditions resulting from such kind of models be supported by Dynare simulation functions (particularly stoch_simul)?

Many thanks!
PD: I’m aware I’ve asked three questions, I think they can be covered in one topic, yet let me know if I should open different topics for each one of them.

Have a look at Shimer’s book “Labor Markets and Business Cycles”. Most of it can be done in Dynare.

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Thanks for the reference!