APP-815: fix: chat context component missing runtime client

[AdityaHegde]

Chat context dropdown is handled by tiptap so it is rendered outside of svelte component tree. So we need to explicitly pass runtime client as context.

Checklist:

• Covered by tests
• Ran it and it works as intended
• Reviewed the diff before requesting a review
• Checked for unhandled edge cases
• Linked the issues it closes
• Checked if the docs need to be updated. If so, create a separate Linear DOCS issue
• Intend to cherry-pick into the release branch
• I'm proud of this work!

[ericpgreen2]

Thanks for catching this!