When doing a SSO login/test, the AD FS page/dialog prompts to enter username and password for authentication. At this step, the Windows integrated authentication is actually expected to use the logged in windows domain credentials for automated authentication. (With Internet Explorer/Edge it works).
Applying the following command on an admin powershell on the ADFS Server should solve the authentication problem for Chrome/Firefox:
Set-ADFSProperties -WIASupportedUserAgents (((Get-ADFSProperties).WIASupportedUserAgents)+'Mozilla/5.0')
This essentially adds Chrome/Firefox to the allowed User Agents on AD FS to enable authentication via Windows integrated authentication. That should work with all modern versions of Chrome/Firefox.
Please find more background here: Configure browsers to use Windows Integrated Authentication (WIA) with AD FS