Fonts in browsers are set independently from fonts in DE. For example, in Firefox they are set in:
Preferences --> General --> Fonts and Colors --> Advanced... --> Fonts for (select one by one all Writing Systems you use)
and for each single Writing System set Proportional, Serif, Sans-serif, Monospace fonts.
To match Fira Comp font in Plasma, the Monospace font in Firefox should be set to Fira Comp as well - for the Writing System used by the page with code you're browsing.