FWIW, before Google Chrome, Firefox was originally Firebird (changed for name collision reasons), and Mozilla had broken off the rest of the Netscape-ish "communications suite" into Thunderbird, both arguably named after cars.
Besides the use of chrome by Netscape/Mozilla that you mention, roughly around that time I heard it used by HCI people to refer flashy GUI design for cosmetics rather than function, and specifically to changes in a particular MacOS version.
I wonder whether Netscape/Mozilla jokingly then used it as a term for the GUI toolkit "trim" around the browser page. Given that this was a transition to the important stuff being on the Web page, rather than your computer. And/or whether Google did.
Mozilla named the web program Phoenix for rebirth. A company objected. Mozilla renamed it Firebird because phoenix was a fire bird. They named the mail program Thunderbird for similarity of Firebird.
The browser was considered slow and bloated however, and when Firefox came, its lack of theme support was perceived as part of it having been de-bloated.
Not wanting to admit term was taken from competing browser is perfectly fine explanation