It probably should be possible to achieve this functionality in Firefox, using this API, but would unfortunately require a new implementation that uses WebRequest instead of CDP. But probably worth looking into!
The archive replay using ReplayWeb.page should work in Firefox and Safari.
Edit: Another limitation on Firefox is lack of service worker support from extensions origins (https://bugzilla.mozilla.org/show_bug.cgi?id=1344561).
This is needed to view what you've archived in the extension. Would need to work around this issue somehow until that is supported, so probably a bit of work, unfortunately.
The archiving is done via the CDP Fetch domain (https://chromedevtools.github.io/devtools-protocol/tot/Fetch...), as it requires intercepting and sometimes modifying the response body of a request to make it more replayable.
Firefox doesn't current support this yet (https://bugzilla.mozilla.org/show_bug.cgi?id=1587426), although, it does have webRequest.StreamFilter instead (https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/Web...), which is lacking in Chromium.
It probably should be possible to achieve this functionality in Firefox, using this API, but would unfortunately require a new implementation that uses WebRequest instead of CDP. But probably worth looking into!
The archive replay using ReplayWeb.page should work in Firefox and Safari.
Edit: Another limitation on Firefox is lack of service worker support from extensions origins (https://bugzilla.mozilla.org/show_bug.cgi?id=1344561). This is needed to view what you've archived in the extension. Would need to work around this issue somehow until that is supported, so probably a bit of work, unfortunately.