E2E: Add Orchestrated SM code_suggestions_in_web_ide_spec

What does this MR do and why?

Relates to https://gitlab.com/gitlab-org/quality/quality-engineering/team-tasks/-/issues/2375

This MR creates a new Self-managed context for the E2E test ee/browser_ui/3_create/web_ide/code_suggestions_in_web_ide_spec.rb to allow the test to run against a self-managed GitLab instance in the Test::Integration::AiGateway orchestrated scenario.

Test pipelines:

• Staging smoke job showing tests are passing: https://ops.gitlab.net/gitlab-org/quality/staging/-/jobs/12675238
• Canary smoke job showing tests are passing: https://ops.gitlab.net/gitlab-org/quality/canary/-/jobs/12675708 (failures in this job with other tests are unrelated to these changes)

MR acceptance checklist

Please evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

1. Check out this branch locally
2. Export the following env vars:

export GITLAB_LICENSE_MODE=test
export QA_EE_ACTIVATION_CODE=<value from 1Password>
export GITLAB_QA_ADMIN_ACCESS_TOKEN=<value from https://gitlab.com/gitlab-org/gitlab-qa/-/blob/master/support/data/admin_access_token_seed.rb#L7>
export QA_SKIP_PULL=true

1. Build the QA image with

docker build -t gitlab/gitlab-ee-qa:your-custom-tag --file ./qa/Dockerfile ./

1. Tag the current nightly build for the corresponding GitLab image

docker tag gitlab/gitlab-ee:nightly gitlab/gitlab-ee:your-custom-tag

1. Run the following from the qa directory:

gitlab-qa Test::Integration::AiGateway gitlab/gitlab-ee:your-custom-tag