Make the bottom dock a real panel

[rajanbor]

Change

The bottom dock was a list of lines under a thin strip. The sandbox owning a pane was legible only from the tab's name, the policy banner reprinted above every render, the input sat in a bar detached from its own output, and there was no way to make it bigger.

It is a panel now:

• Three tabs — Problems, Output, Terminal — underlined rather than boxed, with actions on the right.
• Sessions down the side in the terminal tab, each naming its sandbox and state, so the tab strip stops carrying it.
• The policy stated once, at the head of that session's log, with its shell and working directory.
• The prompt inside the stream, as the last line, which is how a shell actually reads. Clicking anywhere in the stream focuses it.
• Maximise and restore, plus clear, split and new — the last two reporting the reason they cannot run.

Maximised, the panel turns opaque (--bg-sidebar): with the panel material alone you could read the view through it, which is not a panel.

Problems and Output are not placeholders

Problems gathers what the snapshot already says is broken, and every row names the path it was read from:

Source	What it reports
models/*	not ready to answer, with the reason and the requirement
providers/*	not connected
library/skills/*	a permission the skill does not have
library/mcp/*	blocked or otherwise not connected, with its scopes
sandboxes/*	no account of its own — the account boundary would refuse it
capabilities/modules/*	planned rather than built

Errors first, then warnings, then what is merely worth knowing. lib/problems.ts derives it; nothing is invented.

Output keeps every refusal and reason this window reported, after the toast carrying it has gone — in memory only, and the tab says durable logs belong to the daemon.

Validation

• pnpm build (style check, Next build, TypeScript) clean.
• In the browser: ⌘J opened the panel, the tallies read 2 · 3 · 7 for problems and 2 for terminals; switched tabs; maximised and restored; confirmed the maximised panel is opaque in light and dark; ran help and a refused command in a session and watched the prompt stay at the end of the stream.

Security impact

None. It reports refusals that already existed, and it still refuses every command that would need a live pty — a new terminal and a split terminal report the same reason.

Closes #63.