Fix HTML body and inner-message rendering in the chat surface

easterbrooka patched the message rendering path to fix how assistant turns compose HTML bodies and how nested sub-messages get displayed. No diff was captured, but the branch name points at both problems sharing a common root.

The branch targets two distinct rendering problems at once: the outer message's HTML body not rendering correctly, and inner messages - replies, quoted context, or sub-turn content - breaking against the wrong template or losing their nesting structure. Fixing both in a single commit suggests they shared a root cause somewhere in the rendering pipeline.

Typical failure modes here are content getting stripped by sanitisation that's too aggressive, missing wrappers causing layout breakage, or a template lookup that doesn't account for nested message types. The fix addresses the HTML composition path and whatever was responsible for inner messages falling through.

The merge happened nine seconds after the PR was opened - no review, no description. Standard pattern for easterbrooka pushing a known fix on a visible UI regression.