Run the product checks against every host on each pull request

[TarikGul]

The product checks currently run against this repository's own playground. That proves the
core works, not that a host works, so a change can pass CI here and still be broken on a
host.

Once the hosts are in-tree, the same checks should run against each of them, so a core
change is exercised through every host's own runtime rather than only through the reference
one.

Steps

• Run the existing product checks against each host
• Gate each run on that host's change output
• Report per host so a failure names which one broke

Done when

A core change that breaks one host's product path fails that host's check, not just the
reference one.