[CI] Don't rely on github.event_name in devops/actions/run-tests/e2e/action.yml

[aelovikov-intel]

This effectively reverts

"[CI] Use E2E container binaries in run-only manual E2E task dispatch (#19744)"

The problem is that github.event_name corresponds to the top-level workflow, not how .github/workflows/sycl-linux-run-tests.yml was triggered, effectively doing the wrong thing for the manual dispatch of (at least) post-commit workflow.

Instead of that, add a new fake input parameter for the workflow_call trigger in sycl-linux-run-tests.yml to use as the condition.

[aelovikov-intel]

Testing data here. First, for context, post-commit mostly runs tests in full-mode, with only SPIR-V backend being run in run-only mode. As such, SPIR-V backend is the only one failing with trunk if manually dispatching a post-commit workflow (https://github.com/intel/llvm/actions/runs/19118889405/job/54635596621):

> Run mkdir build-e2e llvm
tar (child): /sycl-prebuilt/e2e_binaries.tar.zst: Cannot open: No such file or directory
tar (child): Error is not recoverable: exiting now
tar: Child returned status 2

With these changes (pass for SPIR-V backend job): https://github.com/intel/llvm/actions/runs/19139553978

Manual dispatch of sycl-linux-run-tests (https://github.com/intel/llvm/actions/runs/19141271517/job/54706711731):

# as expected:
> Run ./devops/actions/run-tests/e2e
  with:
    ref: 1651e1a9fb19cd0cb3f8065f1ac977bac34870bd
    binaries_artifact: in-container                         # << this line
...
> Run mkdir build-e2e llvm
  mkdir build-e2e llvm
  tar -I 'zstd' -xf /sycl-prebuilt/e2e_binaries.tar.zst -C build-e2e  # << And those two
  tar -I 'zstd' -xf /sycl-prebuilt/e2e_sources.tar.zst -C llvm

[aelovikov-intel]

Failures on ABI compatibility jobs are known/unrelated: #20537 (comment)