Obviously right after I created this question:

How do I fix SerializationNotSupportedParentType and ThrowNotSupportedException_ConstructorContainsNullParameterNames exception in System.Text.Json?

I find this question. The answer I came up with is this:

A workaround to fix this without changing anything else is to insert the following in your WebClient project file:

<PropertyGroup>
    <_ExtraTrimmerArgs>--keep-metadata parametername</_ExtraTrimmerArgs>
</PropertyGroup>

The real issue should be fixed in https://github.com/dotnet/runtime/issues/81979