Diagnostic build log not emitting properties anymore?

### Issue Description

We first noticed this through Maestro bumps:

* https://github.com/xamarin/xamarin-android/pull/6029
* https://github.com/xamarin/xamarin-android/pull/6034

We have a unit test that is asserting several MSBuild properties are in the diagnostic MSBuild log:

[build.zip](https://github.com/dotnet/msbuild/files/6697116/build.zip)

It's looking for text like `AndroidSdkBuildToolsVersion = `. I see this as parameters to tasks, but that's it.

That's when I noticed I'm seeing env vars in this log but not properties? Did we regress on that? Thanks!

### Steps to Reproduce

I think, just build a project with `/flp1:LogFile=build.log;Verbosity=diag` and look for properties in the file?

### Expected Behavior

Properties are in diagnostic build logs.

### Actual Behavior

I don't see properties in diagnostic build logs?

### Versions & Configurations

.NET 6.0.100-preview.6.21321.13

### Attach a binlog

I don't really see properties in here either:

[msbuild.zip](https://github.com/dotnet/msbuild/files/6697156/msbuild.zip)

No source file or test is named. Reproduce with a project build using `/flp1:LogFile=build.log;Verbosity=diag`, then compare the diagnostic log and attached binlog for MSBuild properties such as `AndroidSdkBuildToolsVersion`. Done means diagnostic build logs emit the expected properties again.

Written by the indexing model from the issue text.