web-ui: count badges and strictly scoped tool views on the session top bar (#501)

The session top bar's tool buttons become icon-only with a small count badge showing how many crons, files, apps, or skills exist in the current context; a zero count shows no number, and the memory and keychain buttons stay bare. The skills view opened from a session's bar now lists only that context's skills — previously org-wide skills were mixed in, which made the view look unscoped.

**Deployment notes**

Web-UI only, but one visible behavior flip: the Skills view opened from a session's top bar now
lists only that context's skills, dropping org-level skills users previously saw there

Depends on #485 — do not merge until it lands.

<!-- codesmith:footer -->
---
<a href="https://app.blacksmith.sh/yc-software/codesmith/qm/pr/486"><picture><source media="(prefers-color-scheme: dark)" srcset="https://pr-comments-assets.blacksmith.sh/codesmith/view-with-codesmith-dark-v2.svg"><source media="(prefers-color-scheme: light)" srcset="https://pr-comments-assets.blacksmith.sh/codesmith/view-with-codesmith-light-v2.svg"><img alt="View with [code]smith" src="https://pr-comments-assets.blacksmith.sh/codesmith/view-with-codesmith-dark-v2.svg"></picture></a> <a href="https://backend.blacksmith.sh/track/enable-autofix?expires=1789249500&installation_model_id=19911&pr_number=486&repository=yc-software%2Fqm&return_to=https%3A%2F%2Fgithub.com%2Fyc-software%2Fqm%2Fpull%2F486&signature=0c6e333ce12a86a04aec88d421af502ec4d9f27f502968151a4bc04d9bb10cb2"><picture><source media="(prefers-color-scheme: dark)" srcset="https://pr-comments-assets.blacksmith.sh/codesmith/autofix-with-codesmith-dark.svg"><source media="(prefers-color-scheme: light)" srcset="https://pr-comments-assets.blacksmith.sh/codesmith/autofix-with-codesmith-light.svg"><img alt="Autofix with [code]smith" src="https://pr-comments-assets.blacksmith.sh/codesmith/autofix-with-codesmith-dark.svg"></picture></a>
<sup>Need help on this PR? Tag <code>@codesmith-bot</code> with what you need. Autofix is disabled.</sup>

<!-- codesmith:autofix:disabled -->
<!-- /codesmith:footer -->