Azure.AI.FormRecognizer 4.1.0 requires at least Azure.Core 1.34.0. Azure Core requires at least System.Diagnostics.DiagnosticSource 6.0.1 for .NET Framework 4.7.2 or higher. Since you are targeting 4.8.1 you cannot downgrade DiagnosticSource to 6.0.0. Why are you trying to downgrade?
Downgrading packages can get tricky because of binding redirects. If you want to downgrade to Azure.AI.FormRecognizer 4.0.0 then downgrade the package using NuGet Package Manager. After that you'll need to fix up the binding redirects. I assume that you have an app/web.config file for your executable. Inside there is a binding redirect element that lists all the assemblies that you rely on and their version. You need to adjust the binding for any package you downgrade to use the version of the assembly that you are now targeting. As example if you updated to 4.1.0 then you most likely had something like this.
<dependentAssembly>
<assemblyIdentity name="Azure.AI.FormRecognizer"
publicKeyToken="..." culture="en-us" />
<bindingRedirect oldVersion="0.0.0.0-4.1.0.0" newVersion="4.1.0.0" />
</dependentAssembly>
You'll need to change the old and new versions to be 4.0.0.0
. You'll need to do that for all the dependencies you downgrade as well. Be aware that sometimes a Nuget version doesn't match the assembly version. You have to use the assembly version. You should search the remaining sections of the config file to see if the assembly is referenced elsewhere as there may be additional references to the versioned assembly you need to update.