To set Microsoft Edge as the default browser for .html files and http/https links you have to use an application association file.
Firstly you need to create an .xml file with this content for example.
<?xml version="1.0" encoding="UTF-8"?>
<DefaultAssociations>
<Association ApplicationName="Microsoft Edge" ProgId="MSEdgeHTM" Identifier=".html"/>
<Association ApplicationName="Microsoft Edge" ProgId="MSEdgeHTM" Identifier=".htm"/>
<Association ApplicationName="Microsoft Edge" ProgId="MSEdgeHTM" Identifier="http"/>
<Association ApplicationName="Microsoft Edge" ProgId="MSEdgeHTM" Identifier="https"/>
</DefaultAssociations>
To set Microsoft Edge Beta as the default browser, set ApplicationName to “Microsoft Edge Beta” and ProgId to “MSEdgeBHTML”. To set Microsoft Edge Dev as the default browser, set ApplicationNameto “Microsoft Edge Dev” and ProgId to “MSEdgeDHTML”.
For domain joined devices you have to configure a group policy for the default file type and protocol associations configuration file:
- Open the Group Policy editor and go to the Computer Configuration\Administrative Templates\Windows Components\File Explorer.
- Select Set a default associations configuration file.
- Click policy setting, and then click Enabled.
- Under Options:, type the location to your default associations configuration file.
- Click OK to save the policy settings.
The example in the next screenshot shows an associations file named associations.xml placed in the sysvol network share.
Default location of the associations file c:\windows\system32\defaultassociations.xml but I choose to put it in the \\sysvol\<domain>\ scripts directory.
The policy creates a Registry key at location :
Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows\System\DefaultAssociationsConfiguration
To check if the policy correctly applied to your system you may check if this reg key exists.
More information can be found here :
https://docs.microsoft.com/en-gb/DeployEdge/edge-default-browser