VS 2019: how to disable warning 'Please install the
'Microsoft.TypeScript.MSBuild' NuGet package to enable TypeScript
compilation in your project.'
You can use NoWarn msbuild property to suppress this warning.
Solution
Add this in your xxx.csproj file:
<PropertyGroup>
<NoWarn>xxx(the related waning code like cs0219)</NoWarn>
</PropertyGroup>
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Update 1
Since the warning does not have a number, you cannot use NoWarn to suppress it.
Instead, you can use
<WarningLevel>0</WarningLevel>
However, it will suppress all the warnings in your project. For your issue, it is the best way but still has some drawbacks if you want the other warnings.
As a suggestion, you could create a new configuration called Test
(Build-->Configuration Manager-->click your project and click New under Configuration drop down box)
, then add these in xxx.csproj file:
<PropertyGroup Condition="'$(Configuration)'=='Test'">
<WarningLevel>0</WarningLevel>
</PropertyGroup>
You can use the Test Configuration to build your project and it will suppress the warning.
If you want to see the other warnings or handle other warnings, you can switch to Debug or Release mode to build your project.
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Update 2
After a deep research, I have reproduced your issue in my side:

Since you do not specify the TypeScript version in MSBuild of VS so that the error occurs.
The cause of it is that you have set the Build Action of the typescript files to TypeScript file. If you set to it, MSBuild will identify them and let MSBuild to use Type Script to build them. Since you do not use TypeScript of MSBuild, so the error happens.
Solution
You can set the Build Action of every typescript file to Content and add custom tool to npm run typescript.

Then restart your project to test again and I am sure that the error will go away.