Global Styles not using some selected fonts in certain themes

Quick summary

A user is trying to update their Headings font on Zoologist to Montserrat, but the changes are not showing on the live site even though they are saving correctly in the Site Editor.

I can replicate this on my Simple Site as shown here:

https://user-images.githubusercontent.com/51870544/210429672-9f3000db-f652-477b-b0b4-1b8e74e769e5.mp4

I tried to check on an atomic site, but it's only showing two fonts for some reason (possibly related to GDPR? not sure):

Steps to reproduce

Set a simple site to Zoologist theme
Try to change the font in the Global Styles to anything other than default
Check to see if the font updated on the live site

Important: ensure that no individual blocks on the page are using the same font as you selected in global styles. If an individual block on the page is using the same font as you selected in global styles then the font is loaded and it works.

What you expected to happen

The font should show correctly after saving the Global Styles changes

What actually happened

The changes are saved, but not reflected on the live site - they only show as default serif/sans-serif fonts

Context

36494970-hc

Follow-up ticket to different address: 5832285-zd-woothemes

Platform (Simple, Atomic, or both?)

Simple

Theme-specific issue?

Any block theme when using a Jetpack supplied font. e.g. TT3

Any block-based derived theme, specifically Zoologist

Browser, operating system and other notes

Firefox, Safari, Chrome

Reproducibility

Consistent

Severity

Most (> 50%)

Available workarounds?

No but the platform is still usable

Workaround details

If the page uses the font on a specific block rather than via global styles then the font will be loaded. Consider changing a heading or paragraph block in the header or footer to use the same font.

Automattic / wp-calypso