ArchiveWeb.page is the latest tool from the Webrecorder project. It works as a Chrome (or Brave, or Edge) browser extension or as a standalone Electron app.
There's also an experimental IPFS-sharing feature, which will share whatever was archived via IPFS, which works best in Brave (due to native IPFS support) or the Electron app.
Web archives can also be exported in a random-access friendly format (WACZ, https://github.com/webrecorder/wacz-format) which contains standard WARCs, allowing large archives to be loaded on-demand.
The extension or app is needed to create the web archives, but once created, the archives are accessible/viewable in any modern browser supporting service workers.
The maker of this, Ilya Kreymer, is a true genius and has contributed many software that has furthered the internet archival community. He's single handedly advanced and furthered the web archival community to where it is today. Web archival would be stuck in the stone age if it weren't for him and his projects.
Disclaimer: I'm just a happy user of this extension. It allowed me to archive a complex website that I wanted to browse offline, where other tools failed.
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.
There's also an experimental IPFS-sharing feature, which will share whatever was archived via IPFS, which works best in Brave (due to native IPFS support) or the Electron app.
Web archives can also be exported in a random-access friendly format (WACZ, https://github.com/webrecorder/wacz-format) which contains standard WARCs, allowing large archives to be loaded on-demand.
The extension or app is needed to create the web archives, but once created, the archives are accessible/viewable in any modern browser supporting service workers.