Add more robust checking of make dist.

[Ferroin]

As of right now, our validation of make dist only reliably catches issues resulting from mandatory components in the install failing.

However, we now have a number of important optional components that we need to verify work correctly.

As a result, we need to update our checking to more robustly verify that installing from a tree prepared with make dist pulls everything in correctly.

[prologic]

@Ferroin The "Checks / Dist" workflow is now migrated to GHA. Can you elaborate on what's needed here?

[Ferroin]

It needs #8382 merged and that flag needs to be used for the make dist builds. However, #8382 is effectively blocked pending completion of #8378, which will resolve the build failures being seen in it.

[prologic]

All yours then :)