Mhv 57145 refactor save reply draft

[fazilqa]

Summary

• Save compose draft scenario has a few flaky tests
• This PR refactors the tests scenario, fixes flaky test and cleanup unnecessary code lines

Related issue(s)

• https://jira.devops.va.gov/browse/MHV-57145

Testing done

• Tests for particular scenario was done by 200x pattern
• All tests run in headless mode without any fails

Screenshots

Note: This field is mandatory for UI changes (non-component work should NOT have screenshots).

	Before	After
Mobile
Desktop

What areas of the site does it impact?

(Describe what parts of the site are impacted if code touched other areas)

Acceptance criteria

Quality Assurance & Testing

• I fixed|updated|added unit tests and integration tests for each feature (if applicable).
• No sensitive information (i.e. PII/credentials/internal URLs/etc.) is captured in logging, hardcoded, or specs
• Linting warnings have been addressed
• Documentation has been updated (link to documentation *if necessary)
• Screenshot of the developed feature is added
• Accessibility testing has been performed

Error Handling

• Browser console contains no warnings or errors.
• Events are being sent to the appropriate logging solution
• Feature/bug has a monitor built into Datadog or Grafana (if applicable)

Authentication

• Did you login to a local build and verify all authenticated routes work as expected with a test user

⚠️ Team Sites (only applies to modifications made to the VA.gov header) ⚠️

• The vets-website header does not contain any web-components
• I used the proxy-rewrite steps to test the injected header scenario
• I reached out in the #sitewide-public-websites Slack channel for questions

Requested Feedback

(OPTIONAL) What should the reviewers know in addition to the above. Is there anything specific you wish the reviewer to assist with. Do you have any concerns with this PR, why?