Move chat integrations to the `Integrations::` namespace [RUN ALL RSPEC] [RUN AS-IF-FOSS]

What does this MR do?

This MR moves all "chat" integrations to the Integrations:: namespace as part of #201855 (closed).

It builds on the groundwork in !60968 (merged) to safely rename STI models.

Does this MR meet the acceptance criteria?

Conformity

• [-] I have included a changelog entry, or it's not needed. (Does this MR need a changelog?)
• [-] I have added/updated documentation, or it's not needed. (Is documentation required?)
• [-] I have properly separated EE content from FOSS, or this MR is FOSS only. (Where should EE code go?)
• [-] I have added information for database reviewers in the MR description, or it's not needed. (Does this MR have database related changes?)
• I have self-reviewed this MR per code review guidelines.
• This MR does not harm performance, or I have asked a reviewer to help assess the performance impact. (Merge request performance guidelines)
• I have followed the style guides.

Availability and Testing

• I have added/updated tests following the Testing Guide, or it's not needed. (Consider all test levels. See the Test Planning Process.)
• [-] I have tested this MR in all supported browsers, or it's not needed.
• [-] I have informed the Infrastructure department of a default or new setting change per definition of done, or it's not needed.

Related to #201855 (closed)