[dotnet-watch] Separate build from run

[tmat]

Update tests to use a recent Aspire package that does not require workload installation.

Use combination of dotnet build and dotnet run --no-build instead of dotnet run.
This has two benefits:

• separates build output (only printed out to dotnet-watch console output on build error or in verbose mode) from application output (sent to Aspire console for Aspire resources)
• when restarting subset of processes impacted by rude edit we can build all affected projects first and only when the build succeeds restart the processes.

Use regex to match errors and warnings in dotnet build output (dotnet build prints all output to stdout).

Fixes #44543

[dotnet-policy-service]

Thanks for your PR, @tmat.
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[tmat]

@phil-allen-msft ptal