How to style headings like text?

You want to revoke the default show rule. It’s not supported yet but it’s on the roadmap. See also How can I bypass set/show rules to revert to the default? and the linked GitHub issue.

In the meantime you can apply a show rule that manually undoes the default rules:

#show heading.where(level: 1): set text(1em/1.4)
#show heading.where(level: 2): set text(1em/1.2)
#show heading: set text(weight: "regular")

It’s not very elegant but I think putting that at the top of your document should work fine (i.e. if you change the text style for the whole document, it should also affect the headings as expected).