STR

1. New message, type |John Doe <john@asdf.com>| as recipient (sic; must be longer than edit-pill default length), press Enter -> creates new pill.
2. cursor left to select virgin pill, press Enter to edit

Actual

• cursor not visible (but functional, at the end of label; note that the bug does not occur if your recipient is too short)
• starting from 2nd edit, cursor always visible

Expected

• cursor should be visible also on first edit of a pill

Notes
My display settings on Windows have 140% screen scaling, which may change font sizes.

Thanks for identifying this.
The issue was a tiny shift of 1px in the padding of the pill.
I solved it by removing the inline margin of the label and keeping the padding consistent for each state (editing and non-editing).

Pushed by mkmelin@iki.fi:
https://hg.mozilla.org/comm-central/rev/f7b29a032c0c
Fix the inline padding of the editable recipient pill to not hide the input field cursor. r=mkmelin, ui-r=Paenblab

Unfortunately, this is still happening (again), exactly as described in comment 0:
seen on 76.0a1 (2020-03-29) (64-bit)

• type: |John Doe <john@asdf.com>|, press Enter
• then cursor left, Enter to re-edit.
  --> editing cursor on the right (after .com) not visible

You already opened bug 1627451, there's not need to reopen this as this fix was correct and took care of the issue.
The new issue is a regression caused by something else.