Refactor: Consolidate log streaming logic into centralized `log_utils.follow_logs()`

[andylizf]

In preparation for #4128 (DAG improvements), both jobs and serve modules need log streaming functionality. This refactor provides a centralized utility to avoid duplicating the logic across modules.

We consolidate duplicated log streaming logic from serve_utils into a new utility function log_utils.follow_logs():

• Move basic streaming logic from _follow_logs()
• Add support for custom line handlers

• Refactor _follow_replica_logs() to use the new utility

        Lets left a todo for separate this part into master branch first.

_Originally posted by @cblmemo in https://github.com/skypilot-org/skypilot/pull/4128#discussion_r1833464435_

Tested (run the relevant ones):

• [x] Code formatting: bash format.sh
• [ ] Any manual or new tests for this PR (please specify below)
• [ ] All smoke tests: pytest tests/test_smoke.py
• [ ] Relevant individual smoke tests: pytest tests/test_smoke.py::test_fill_in_the_name
• [ ] Backward compatibility tests: conda deactivate; bash -i tests/backward_compatibility_tests.sh

[andylizf]

@cblmemo PTAL, thanks!

[andylizf]

@cblmemo Please merge this PR or rerun the action - the test failure is due to resource availability as explained in #4308.