One particularly famous incident (after the founder's death) was the Homestead strike [1]. Strike-breaking was very much in the Pinkerton's wheelhouse and it's a good example of what they were actually used for [2].
There doesn't seem to be a lot of fiction that features the Pinkertons prominently. One exception is the (excellent) HBO TV series Deadwood.
It's particularly apropos at this time because the lawless violence and organized labor suppression of the robber barons in the Pinkerton era is very much the future we are careening towards.
[1]: https://www.pbs.org/wgbh/americanexperience/features/carnegi...
[2]: https://allthatsinteresting.com/pinkerton-detective-agency