Stream build process output

Ensure that output and errors from the underlying build command are
streamed for real-time build progress updates and debugging.

This change strips out all code that is currently unecessary and adds
tests for the remaining functionality.

Test: atest --host build_test_suites_local_test build_test_suites_test
Bug: 330365727
Change-Id: I7ef98d6654fe1435cf67c15e2c516a0967e03a75