Manage Nuget Packages for Solution not showing packages installed per project (for .net core 3.1 packages)

[LightVolk]

Details about Problem

NuGet product used (NuGet.exe | VS UI | Package Manager Console | dotnet.exe):

NugetPackageManager 5.4.0
Visual Studio Enterprise 2019 16.4.2
Nuget.exe (on server): 5.3.1

dotnet.exe --version (if appropriate):
1.1.8 [C:\Program Files\dotnet\sdk]
2.1.104 [C:\Program Files\dotnet\sdk]
2.1.200 [C:\Program Files\dotnet\sdk]
2.1.201 [C:\Program Files\dotnet\sdk]
2.1.202 [C:\Program Files\dotnet\sdk]
2.1.302 [C:\Program Files\dotnet\sdk]
2.1.402 [C:\Program Files\dotnet\sdk]
2.1.403 [C:\Program Files\dotnet\sdk]
2.1.500 [C:\Program Files\dotnet\sdk]
2.1.502 [C:\Program Files\dotnet\sdk]
2.1.503 [C:\Program Files\dotnet\sdk]
2.1.504 [C:\Program Files\dotnet\sdk]
2.1.505 [C:\Program Files\dotnet\sdk]
2.1.507 [C:\Program Files\dotnet\sdk]
2.1.602 [C:\Program Files\dotnet\sdk]
2.1.604 [C:\Program Files\dotnet\sdk]
2.1.700 [C:\Program Files\dotnet\sdk]
2.1.701 [C:\Program Files\dotnet\sdk]
2.1.801 [C:\Program Files\dotnet\sdk]
2.1.802 [C:\Program Files\dotnet\sdk]
2.2.101 [C:\Program Files\dotnet\sdk]
2.2.102 [C:\Program Files\dotnet\sdk]
2.2.203 [C:\Program Files\dotnet\sdk]
2.2.300 [C:\Program Files\dotnet\sdk]
3.0.100 [C:\Program Files\dotnet\sdk]
3.1.100 [C:\Program Files\dotnet\sdk]

OS version (i.e. win10 v1607 (14393.321)):
win7

NuGet.Server version: 3.1.2

Worked before? If so, with which NuGet version:
Worked before (search 2.2.* packages) : 4.4.1

Detailed repro steps so we can see the same problem

create bat file:
nuget.exe add %1 -source \nuget-server\nuget_core3
2.
Add 3.1.0 packages like: Microsoft.Extensions.Logging 3.1.0 on server feed

3. Try to search it by Nuget Package Manager.
4. Fail.
   ...

Other suggested things

I can not search any 3.1.* nuget packages, but Microsoft.Extensions.FileProviders.Embedded search (3.1.0 version).
And i can search all core packages 2.2.* version.

Verbose Logs

Other important thing:

I can not push some packages. Not all, just few.

Example:
C:\PushToIntegration_Core3>nuget.exe push "C:\PushToIntegration_Core3\Core3\microsoft.aspnetcore.jsonpatch.3.1.0.nupkg" -source C:\nugetRep\nuget_integration_core3 -verbosity detailed
NuGet Version: 5.3.1.6268
Pushing microsoft.aspnetcore.jsonpatch.3.1.0.nupkg to 'C:\nugetRep\nuget_core3'...
Acquiring lock for the installation of Microsoft.AspNetCore.JsonPatch 3.1.0
Acquired lock for the installation of Microsoft.AspNetCore.JsonPatch 3.1.0
Installing Microsoft.AspNetCore.JsonPatch 3.1.0.

And it stops here. But package add on folder feed.
P.S. after add --verbouse flag - package add (after large timeout, like a minute):

PackageSignatureVerificationLog: PackageIdentity: Microsoft.AspNetCore.JsonPatch.3.1.0 Source: PackageSignatureValidity: True
Completed installation of Microsoft.AspNetCore.JsonPatch 3.1.0
Successfully added package 'C:\PushToIntegration_Core3\Core3\microsoft.aspnetcore.jsonpatch.3.1.0.nupkg' to feed 'C:\nugetRep\nuget_core3'.
Your package was pushed.

[LightVolk]

It seems that this issue is a problem of that.
At Microsoft.Extensions.* 3.1.0 has packageIcon.png dublicate. If remove one of that - it solve problem.