Seems that the issue is not related to Typst show rules, but the bibliography style selected. You can try by testing it with a different bib style:

#let bib = ```bib
@article{bruederle2018,
  title = {Nighttime Lights as a Proxy for Human Development at the Local Level},
  author = {Bruederle, Anna and Hodler, Roland},
  date = {2018-09-05},
  journaltitle = {PLOS ONE},
  shortjournal = {PLoS ONE},
  volume = {13},
  number = {9},
  pages = {e0202231},
  doi = {10.1371/journal.pone.0202231}
}

@article{easterly2003,
  title = {Tropics, Germs, and Crops: How Endowments Influence Economic Development},
  shorttitle = {Tropics, Germs, and Crops},
  author = {Easterly, William and Levine, Ross},
  date = {2003-01-01},
  journaltitle = {Journal of Monetary Economics},
  shortjournal = {Journal of Monetary Economics},
  volume = {50},
  number = {1},
  pages = {3--39},
  doi = {10.1016/S0304-3932(02)00200-3},
  keywords = {Economic development,Geography,Institutions}
}
```.text

#show par: set par(first-line-indent: 1.8em)

#lorem(30)@easterly2003

#lorem(30)@bruederle2018

//#show bibliography: set par(first-line-indent: 0pt)

#bibliography(
  bytes(bib),
  title: "References",
  style: "ieee", //"chicago-author-date"
  full: true,
)

Results:

ieee

chicago-author-date

The styles applied depend on the bib style selected. The Chicago: Author-Date style seems to be rendered appropriately. See https://libguides.williams.edu/citing/chicago-author-date#s-lg-box-21699946 and https://www.chicagomanualofstyle.org/tools_citationguide/citation-guide-2.html