Hello @Pavel yannara Mirochnitchenko thanks for the report on this issue. Looking through the details in some of the other answers and the replies, there are few things to untangle.
First is getting through some of the confusion of managing the legacy version of Microsoft Edge that uses UWP and EdgeHTML (that Microsoft folks sometimes refer to by the project name "Spartan" to for an easier reference name that I'll use here) and the current version of Microsoft Edge running Chromium.
The web post referred to in the Microsoft vendor response https://www.thewindowsclub.com/disable-microsoft-edge-first-run-welcome-page is focused on configuring the legacy version of Edge, not the current version. Please ignore the details in this article. The legacy version of Edge has many very similar policies and the registry location the ADMX targets is confusingly very similar as well.
From your list of policies from your question in the Q&A, it does appear that you are looking at the right documentation and policy names for the current version of Edge but were targeting the wrong registry location in your scripting examples.
In the registry you need to target ✅:
HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Microsoft\Edge
NOT 🚫:
HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\MicrosoftEdge
* Notice the path separator between "Microsoft" and "Edge"
For the policies you listed you are trying to set, here is the contents of a .reg file to set them as an example:
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\Software\Policies\Microsoft\Edge]
"SpotlightExperiencesAndRecommendationsEnabled"=dword:00000000
"DiagnosticData"=dword:00000000
"HideFirstRunExperience"=dword:00000001
"NonRemovableProfileEnabled"=dword:00000000
"PersonalizationReportingEnabled"=dword:00000000
"BrowserSignin"=dword:00000001
"ForceSync"=dword:00000001
"SyncDisabled"=dword:00000000
In my testing of these settings, Microsoft Edge v131.0.2903.99 did not show any first run, or "second chance" first run dialogs on subsequent full restarts of the browser. To note "second chance" first run dialog logic is different for EU DMA regions. I tried to simulate this environment in my testing, but actual conditions may be different.
A few other things to point out.
I was able to find all of the policies you listed within Intune's Settings Catalog. Settings Catalog is Intune's location for setting Edge policies going forward so you should be able to set all this through Intune now and in the future. Here is an example configuration profile from Intune with all the settings:
❗Be mindful of the settings for:
Send required and optional diagnostic data about browser usage - Disabled
The way you have this worded is incorrect if you set it exactly like this to "Disabled". It should be:
Send required and optional diagnostic data about browser usage - Enabled, set to "Off (Not recommended)"
[Note: this question was asked in an internal Microsoft forum as well. This response is a version of a response I made in that forum to provide the information in this more public forum as well]