Describe the bug
A clear and concise description of what the bug is.
To Reproduce
Steps to reproduce the behavior:
File > Properties...Font tab and check Embed fonts in the document. Note that this option may not be present for macOS.Expected behavior
The embedded font should appear
Actual behavior
The text uses a fallback Arial font (as in Microsoft Office 2010, Windows 7 Ultimate)
Environment
Additional context
I really have no idea how to debug this. There have been other reports of issues specifically with LibreOffice and my guess is that there are some bugs in that software. I.e. if it succeeds with embedding the font when it compiles a PDF but fails when compiling a different format, that indicates there's at least an issue with their ODT / DOCX compiler.
Since you have the nice OTF files (with CFF-outlines) installed, it's very possible that the bug is related to CFF outlines and that simply removing the OTF files and installing the TTF files will fix it.
The only difference between the OTF files and the TTF files is that TTF has slightly less precise outlines (the TTF font files uses quadratic bezier curves while the OTF fonts uses cubic bezier curves.) It really shouldn't matter in most cases, so I'd recommend trying to remove the OTF files and installing the TTF files.
@reinhart1010 Would you mind trying out Inter UI release v3.2 to see if this is still an issue? v3.2 was compiled with an updated toolchain that addresses a bug in fonttools which might have caused issues before.
Unfortunately, this issue still exists (Left: actual results, Right: PDF file created on Windows)

Tested in LibreOffice 6.1 in Windows 10 (where file is created), and LibreOffice 6.0 in Ubuntu 18.04 LTS (where screenshot is taken). In Ubuntu the older font version (3.0.0) is installed.
The PDF does look correct though. I thought the issue was that the font would not be embedded in the PDF..?
Did you try installing the TTF files instead of the OTF files?
The PDF was generated on Windows, which the newer font is installed. I use OTF version for both OSes.
So, if I understand the issue correctly:
Expected: LibreOffice to include the font files inside the office file
Actual: The font is replaced by some other locally-available font (it appears that the font was not embedded in the office file)
If these assumptions are correct, what you want to do is this:
Yes, this one is correct.
The problem is LibreOffice not these fonts.
LibreOffice is only embedding the four R/I/B/BI weights for almost all fonts tested.
This includes FOSS and commercial fonts.
You can test with the Source Sans Pro family which is included with LibreOffice.
Create a document which includes all 12 styles, and save it, extract the ODT (ZIP), looks in Fonts folder.
For Source Sans Pro you will only find Regular, Italic, Bold, and Bold Italic (stupidly numbered).
Note I tested on Windows; it may be different on Linux or Mac.
Regarding LibreOffice embedding fonts in PDFs, it _always_ embeds a subset of fonts.
The "Embed Fonts" setting has no effect on this at all.
That setting only affects putting the fonts in the ODT (or DOCX).
The Inter fonts did all embed in the PDF correctly until the BETA fonts were added.
The BETA style group names are so wacko that LibreOffice cannot figure-out what to do.
I renamed the fonts properly so I could test the whole family (as Inter LO).
Now it all works.
Soooo ... this issue is not an Inter fonts issue and can be closed.
Thank you for investigating and explaining @kenmcd