This is far from exhaustive, but hopefully it can get you started! (I'd recommend skimming most of them, then really focusing on those where the application and/or modeling environment is uniquely relevant or interesting for your research.)
General reviews of empirical approaches:
Angrist and Krueger (1999) looks at several methods (including DiD) in the context of labor economics, while Blundell and MaCurdy (1999) also look at DiD in labor, but more from a natural experiment perspective. Chapter 1 in the textbook the Economics of Education (2020) similarly discusses a couple empirical approaches, including DiD, in the context of the education literature. Roberts and Whited (2012) discuss several methods (including IV and DiD) in corporate finance applications. This working paper in the education space looks at a variety of different works that have used various empirical methods to study international standardized test-related outcomes, and might be of interest (mostly for the works it cites). Similarly, this provides a long list of empirical applications of DiD in economics of education.
Papers describing how to properly apply DiD:
I actually have found this paper from the public health world helpful in framing DiD issues previously, so I'll include it here as well. This paper from 2019 is pretty approachable, and might be of interest as well. This paper goes into a bit more depth (I think) than the others, so might be worth looking at.
Specific examples of DiD in use:
A comprehensive list would probably crash the Stack Exchange servers, but some examples (and their particular focus) are: Medicaid on early childhood (2016), food stamps (2016), information regarding food safety (i.e. health scores) on consumer behavior (2002 version linked, published in 2003), "green" advertising on consumer preferences (2010), high school employment on education (with a propensity score matching element) (2008), Nestle's impact on mortality in low income countries (2018), and tracking and educational outcomes (2020). Particularly well-known examples of DiD applications are this Dube Lesterer and Reich example looking at minimum wage, and this Duflo paper looking at a natural experiment related to education in Indonesia. There's also this paper from 2010 that looks at how exposure to Malaria impacts labor market outcomes, and this one from 2015 that examines the impacts of community health centers.
Other papers of interest:
I know you mentioned wanting to avoid the econometric theory, but a few papers I'd recommend looking into (they also include applications) are this paper by Bertrand, Duflo and Mullainathan (2003 version linked, published in 2004), these two papers that look at DiD when the treatment varies over time, and somewhat relatedly, this one that looks at DiD when the treatment intensity varies over time. Finally, this paper that looks at the importance of properly testing for, and dealing with, the potential for parallel trends.