#9122: fix(webchat): constrain .chat-new-messages to button size

## Summary - Fix `.chat-new-messages` element covering the entire chat viewport (1328x1356px) - Constrain it to a properly sized, positioned button/indicator via `width: fit-content` - Prevents invisible click interception on the chat area Fixes #8944 Fixes #8960 ## Test plan - [ ] `pnpm build && pnpm check && pnpm test` passes - [ ] Webchat new-messages indicator is a small button, not a full viewport overlay - [ ] Chat messages are clickable and scrollable without interference 🤖 Generated with [Claude Code](https://claude.com/claude-code) <!-- greptile_comment --> <h2>Greptile Overview</h2> <h3>Greptile Summary</h3> This PR updates the `.chat-new-messages` styling to prevent it from stretching to the full size of its flex-column parent (the chat container), which was causing an invisible overlay that intercepted clicks/scrolls in the chat viewport. It does this by explicitly constraining the indicator to its content width via `width: fit-content` alongside `align-self: center`, applied in both the chat layout stylesheet and the shared components stylesheet so the constraint holds regardless of which stylesheet wins in the cascade. <h3>Confidence Score: 5/5</h3> - This PR is safe to merge with minimal risk. - Changes are narrowly scoped to CSS for a single UI element and consistently apply a content-width constraint in both relevant stylesheets; no functional logic, API, or build configuration is affected. - No files require special attention <!-- greptile_other_comments_section --> _{(3/5) Reply to the agent's comments like "Can you suggest a fix for this @greptileai?" or ask follow-up questions!} **Context used:** - Context from `dashboard` - CLAUDE.md ([source](https://app.greptile.com/review/custom-context?memory=fd949e91-5c3a-4ab5-90a1-cbe184fd6ce8)) - Context from `dashboard` - AGENTS.md ([source](https://app.greptile.com/review/custom-context?memory=0d0c8278-ef8e-4d6c-ab21-f5527e322f13)) <!-- /greptile_comment -->