By definition, incognito mode shouldn't leave a trail of visited websites.
However, HSTS (HTTP Strict Transport Security) requires the browser to keep a database of hosts that have requested HSTS, and honor HSTS for subsequent requests.
This introduces a conflict and there are two possible ways of resolving it:
Browsers always honor HSTS requests made inside an incognito session, even when browsing outside of the incognito session.
Browsers honor HSTS requests made inside an incognito session for that session only.
Which of them is implemented in popular browsers?
Additionally, as discussed in the comments, do HSTS requests outside incognito session affect requests inside incognito session?