I've gone down a rabbit hole regarding the inner workings of Lawnchair's font system over the last couple of days and I think I've figured it out.
The solution is actually quite simple (just rename the internal font's label in the GoogleFontsListing.kt file) but I wanted a better understanding of what's going on to be sure that my solution was not going to break anything.

I'll put together a pull request soon but, in the meantime, I'll put my intentions here:

• Update the internal font from Inter v3.12 to Inter v4.0 (released November 2023... v4 has the same license as v3)
• Label the font "Inter v4" to avoid a duplicate name collision with the Google Fonts "Inter" font
• Update the default/internal font labels (seen on the General page) so that they match the format used when a different font is selected (i.e. append variant name to family name)

(I've already tested this myself in a custom build and it all works great.)

This seems like a good opportunity to update the internal font and keep things up-to-date.
Please let me know if updating the font is OK or too radical an idea. v4.0 is stable and almost indistinguishable from v3.12.

If you'd rather not update the font, please let me know. I could just name the internal font "Inter v3" instead.
Thanks.

Back to the drawing board... Unless the label matches the actual font name, the variant styles do not display correctly in the drop-down menu or in the default/internal font labels (on the General page). It's a small thing but it's a backward step.

Incidentally, the drop-down variant menu for the internal font lists 3 different italic variants, none of which are actually available. Also, the drop-down variant menu quite often needs to be opened twice to see the actual variant styles.

I can see why the font section is labelled 'experimental'.
I'll keep thinking about things though and if I come up with anything, I'll post back.

(We could still update the internal font without breaking anything, though.)

Perhaps the easiest solution would be to filter the Inter font from the Google Fonts list (so that there is only one Inter font: the internal one) and then add the missing variants to the internal Inter font so that they match all the variants that were available in the Google Fonts version.

On further investigation,. both Inter entries use the Google Fonts version (neither uses the internal version), even though they have different sets of variants. Tested by replacing the internal Inter font files with an Inter Italic variant (which is not available in the Google Fonts version of Inter). The italic variant is used on first startup but not seen again when selecting either of the Inter versions from the font list (it is possible to separate the radio buttons if the variants of the two versions don't match).

With this in mind, I think the easiest option might be to simply remove the second Inter entry (leaving the original Google Fonts version).
The only drawbacks are that if the Google Fonts somehow don't load, then the font list would be empty and there would be no way to reinstate the internal Inter font after choosing a custom font (via TTF or OTF file), but this seems to be the case at the moment anyway.

I think I'll leave this to the devs for the time being.
After all, the font section is still experimental.

Edit:
If the Google Fonts did not load, the font list would not be empty... the three sans-serif system fonts would still be there.

I'm still working on this (deeper down the rabbit hole)...

I should soon be able to put together a PR which addresses several different font issues:

1. Testing shows that both Inter fonts currently listed in the font list are the same Google Font (but shown with different variants). Neither is the internal Inter font.
2. The 2nd Inter font entry lists italic variants which are not available. This font entry can be removed from the list completely.
3. The internal Inter font can be updated (from v3.12 to v4.0) and added to the font list (with all 18 available variants) so that users can revert to the default font if desired.
4. The internal Inter font can be renamed (perhaps "Inter v4.0") to differentiate itself from the Google Fonts version.
5. When a font is selected, the family and variant are both displayed on the General settings page with the exception of the default font which reads "Inter" instead of "Inter Regular". (Easy fix.)
6. When first visiting the font list, no radio button is selected. The default font should be listed and selected. Item 3 above will fix this.
7. During testing, I notice that AssetFont and ResourceFont font types cannot be added to the font list without issue. When first selecting one of these font types (which don't actually appear in the font list at the moment), the radio button is selected but when leaving the font list, the font is not applied and going back to the font list, the radio button is no longer selected. I'll fix this not-yet-a-bug as I plan to add the internal Inter font to the font list as a ResourceFont.
8. The Google Fonts list can be updated (with 78 new fonts).

It's still a work-in-progress but it's taking shape and tests are going well. I just thought I'd give anyone following this issue an update to let them know that I've not abandoned it.