[JS API] Catch C++ error in js api async compile_model (#34771)
### Details:
- Add tests
- Forward errors from C++ API in `compile_model()`
- Unskip tests for `compile_model()` and other non async methods tested
in _basic.test.js_ `CVS-180810`
### Tickets:
- *ticket-id*
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Co-authored-by: Pawel Raasz <pawel.raasz@intel.com>