refactor: add handlers to `manifest push` commmand

[wangxiaoxuan273]

What this PR does / why we need it:

Which issue(s) this PR fixes (optional, in fixes #<issue number>(, fixes #<issue_number>, ...) format, will close the issue(s) when PR gets merged): Part of #1542

Please check the following list:

• [x] Does the affected code have corresponding tests, e.g. unit test, E2E test?
• [ ] Does this change require a documentation update?
• [ ] Does this introduce breaking changes that would require an announcement or bumping the major version?
• [ ] Do all new files have an appropriate license header?

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 85.00000% with 6 lines in your changes missing coverage. Please review.

Project coverage is 84.01%. Comparing base (2703462) to head (2f10233).

Files with missing lines	Patch %	Lines
cmd/oras/root/manifest/push.go	40.00%	3 Missing and 3 partials :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #1555 +/- ## ========================================== - Coverage 84.02% 84.01% -0.01% ========================================== Files 119 119 Lines 5315 5343 +28 ========================================== + Hits 4466 4489 +23 - Misses 602 606 +4 - Partials 247 248 +1 ```

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[qweeah]

@wangxiaoxuan273 Can you help resolve the conflict?