Move "test settings" code from integration_settings_form.js to Vue component

What does this MR do and why?

This MR is part 3 of of #342121 (closed), an effort to remove app/assets/javascripts/integrations/integration_settings_form.js and move its current responsibilities to Vuex or existing Vue components.

• Part 1: !75484 (merged).
• Part 2: !75838 (merged)

In this MR, we remove the TEST_INTEGRATION_EVENT from the integration form event hub and related Vuex actions/mutations/state. We move all of the "test integration" functionality to integration_form.vue.

There are no user-facing changes in this MR.

Screenshots or screen recordings

Error state	Success state
Error_state	test-success

How to set up and validate locally (optional)

1. Enable and configure the Jira integration for the project. More information.
2. Click test settings. The Save button should be disabled and the Test button should be loading while the request is in-flight. Once done, you should get a toast message Connection successful.
3. Play around with various states of the form (incomplete form, invalid form, etc.).

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.

Related to #342121 (closed)