[bobleer]

Summary

Correct five presentation issues reported during verification of #3539, with one commit per issue:

• Center the unused-session usage state within its modal instead of leaving it aligned to the left.
• Render calendar day cells as localized numbers without the Chinese date suffix, while retaining full-date accessibility labels.
• Keep unsupported WSL options disabled without displaying a redundant explanatory row. Checking and discovery-failure/retry states remain visible.
• Remove the repeated local computer name from the workspace source selector. Peer mode still identifies the executing remote device.
• Hide the corner assistant launcher whenever a FlowChat scene is visible, including when the other pane has focus. Keep the retained conversation dock mounted and show its launcher on other screens.

Verification

AI-assisted implementation, automated checks and native macOS debug verification.

• pnpm run check:web passed, including type-check and Appearance/theme audits.
• 160 focused tests across nine files passed: session usage/modal, date picker, project creation, SSH dialog/fields, WSL capability routing and floating conversation activity/isolation. Existing visibility expectations were updated to match the requested UI.
• ESLint on the changed production TSX files passed.
• git diff --check and the Git object-size check passed.
• Native debug verification confirmed the centered modal, numeric calendar cells with full-date accessibility labels, disabled WSL without a hint, no repeated local hostname, and no corner launcher with a conversation alone or alongside a focused file pane. The launcher remains available on the task board. No AI turn, scheduled task or project was created for these checks.

Remote scenarios: Peer identity and WSL host routing are covered by local fixtures; live SSH, Peer, Remote Connect and Detached Dispatch were not exercised. No persisted shape, transport or runtime behavior changed. Native verification screenshots are retained locally outside the repository.