Microsoft Chromium-based Edge supports "Edit and Replay" requests in the Network Tab as an experimental feature:
In order to enable the option you have to "Enable Experimental Features".
Control+Shift+I (Windows, Linux) or Command+Option+I (macOS)
and tick the checkbox next to "Enable Network Console".
More details about how to Enable Experimental Tools and the feature can be found here
Update (April 2023): This is no longer an experimental feature in Edge and it is available by default