Looking for books on the Hittites, their origins, the political and military history of their empire, and anything that we know about Hittite economy, religion, society, daily life and culture.
I already have Trevor Bryce's The Kingdom of the Hittites and Life and Society in the Hittite World.
You've already got probably the best place to start with Bryce's Life and Society. The bibliography from there is 20 years old, but there are not any major new comprehensive monographs on the Hittites since then. The Collins (below) is slightly more recent. Between those two, the bibliography will be very good. Some others which are also relatively recent:
Collins, The Hittites and their World (Leiden: Brill, 2008)
Hoffner, The Laws of the Hittites: a critical edition (Leiden: Brill, 1997)
Macqueen, The Hittites and their Contemporaries in Asia Minor (London: Thames and Hudson, 1986)
Rutherford, Hittite texts and Greek religion: contact, interaction, and comparison (Oxford, 2020)
Bilgin, Officials and administration in the Hittite world (de Gruyter, 2018)
Imparati, Studi sulla società e sulla religione degli Ittiti (Firenze: LoGisma, 2004)
Haas, Geschichte der hethitischen Religion (Leiden: Brill, 2004)
Klengel, Geschichte des hethitischen Reiches (Leiden: Brill, 1998)
Roos, Hittite Votive Texts (Leiden : Nederlands Instituut voor het Nabije Oosten, 2007)
Beckman, Hittite Diplomatic Texts (Atlanta: Scholars, 1995)
Weeden and Ullmann, eds, Hittite landscape and geography (Leiden: Brill, 2017)
Cammarosano, At the interface of religion and administration: the Hittite cult inventories (Wiesbaden: Harrassowitz Verlag, 2021).
Beyond all Boundaries: Anatolia in the first millennium BC (Leuven: Peeters, 2021)
International HFR Symposium, Cult, temple, sacred spaces: cult practices and cult spaces in Hittite Anatolia and neighboring cultures (Wiesbaden, Harrassowitz Verlag, 2020)
Hout, A history of Hittite literacy: writing and reading in late Bronze-age Anatolia (1650-1200 BC) (Cambridge 2020)
Glatz, The making of empire in Bronze Age Anatolia: Hittite sovereign practice, resistance, and negotiation (Cambridge 2020)
u/Alkibiades415 gave you some great suggestions. You should definitely start with Bryce's books and/or the introductory overview by Billie Jean Collins, as they are by far the most readable and up-to-date overviews of Hittite history and society.
I provided a few other recommendations in I am fascinated by the Hittites. Are there any good books that go into depth about them? Notable publications since that post include Handbook Hittite Empire: Power Structures edited by Stefano de Martino and, if you read German, Manfred Hutter's Religionsgeschichte Anatoliens.