How can I find the face of the items in the headeline in lsp-mode?

Re-edited the answer for clarity

Typically I would put my cursor over the text, and call M-x describe-face, but I can't do that with the headerline.

In the above screenshot, I want to change the headerline to something contrasting. If I could change the light grey to something darker, it would do the job. So I tried to identify the base faces. So far I found these 3:

1. lsp-headerline-breadcrumb-path-face: underlined in red
2. lsp-headerline-breadcrumb-separator-face: the > separator, underlined in yellow (but invisible because it disappears into the background)
3. lsp-headerline-breadcrumb-symbols-face: underlined in cyan

But I can't figure out the spaces in between. If I change the *-symbols-* and *-path-* faces listed above by adding :background "brightblack", and *-separator-* to just :foreground "black", I can only change the underlined parts (see screenshot below).

I also looked at the results of list-faces-display (without my customisation), there is no light grey background (see screenshot below). So I think something other than these faces is giving the light grey background, if I could change that, I wouldn't need to change them individually or find the face for the intermediary spaces.

Follow-up to NickD's question:

header-line-format is set to:

((t  (:eval   (window-parameter nil 'lsp-headerline--string))))

When I try to get the value of lsp-headerline--string with C-h v, I get the message [No match].