refactor: organize frontend components into features/ directories

Moved 43 component files into 9 feature domains:
- features/git/ — commit-dialog, commit-panel, file-editor, git-mount-editor,
  git-toolbar, merge-dialog
- features/project/ — repositories-settings-tab, repository-create-dialog
- features/terminal/ — special-keys-panel, special-keys-strip,
  terminal-session-tabs, terminal
- features/workspace/ — workspace-card, workspace-create-form,
  workspace-header, workspace-instance-chips
- features/session/ — create-session-form, session-card, session-list
- features/tool/ — instance-list, manifest-editor, start-tool-fab,
  start-tool-modal, tool-starter, tools-bottom-sheet
- features/notification/ — event-toast-bridge, notification-center,
  notification-item
- features/settings/ — settings-tab-layout
- features/mobile/ — mobile-action-sheet, mobile-detail-view, mobile-edit-view,
  mobile-fab, mobile-list-view, mobile-nav, mobile-page-header,
  mobile-terminal-header, mobile-terminal-wrapper

Updated all imports across pages and components.
Root components/ now only contains generic UI pieces:
app-shell, code-editor, data-states, icon, protected-route, syntax-highlighter.

Quality gates: verified no remaining old imports.

apps/web/src/components/features/tool/start-tool-fab.tsx

@@ -0,0 +1,118 @@
+/** Floating action button to start a tool from any page. */
+
+import { useState } from "react";
+import { Icon } from "./icon";
+import { ToolStarter } from "./tool-starter";
+import type { Workspace } from "../types/workspace";
+import { listAllWorkspaces } from "../api/workspaces";
+
+export function StartToolFAB() {
+	const [open, setOpen] = useState(false);
+	const [workspaces, setWorkspaces] = useState<Workspace[]>([]);
+	const [workspacesLoading, setWorkspacesLoading] = useState(false);
+	const [selectedWorkspace, setSelectedWorkspace] = useState<Workspace | null>(
+		null,
+	);
+
+	const handleOpen = async () => {
+		setOpen(true);
+		setWorkspacesLoading(true);
+		try {
+			const data = await listAllWorkspaces();
+			setWorkspaces(data);
+		} catch {
+			// ignore
+		} finally {
+			setWorkspacesLoading(false);
+		}
+	};
+
+	const handleClose = () => {
+		setOpen(false);
+		setSelectedWorkspace(null);
+	};
+
+	return (
+		<>
+			<button
+				className="start-tool-fab"
+				onClick={handleOpen}
+				title="Start a new tool"
+				type="button"
+				aria-label="Start a new tool"
+			>
+				<Icon name="play" size="md" />
+			</button>
+
+			{open && (
+				<div className="modal-overlay" onClick={handleClose}>
+					<div
+						className="modal-content start-tool-modal"
+						onClick={(e) => e.stopPropagation()}
+					>
+						<div className="modal-header">
+							<h3>Start Tool</h3>
+							<button
+								className="ghost-button small"
+								onClick={handleClose}
+								type="button"
+								aria-label="Close"
+							>
+								<Icon name="close" size="sm" />
+							</button>
+						</div>
+
+						{workspacesLoading ? (
+							<p className="muted">Loading workspaces...</p>
+						) : workspaces.length === 0 ? (
+							<p className="muted">
+								No workspaces yet.{" "}
+								<a href="/workspaces">Create a workspace first</a>.
+							</p>
+						) : !selectedWorkspace ? (
+							<div className="form-group">
+								<label htmlFor="fab-workspace-select">Select a workspace</label>
+								<select
+									id="fab-workspace-select"
+									value=""
+									onChange={(e) => {
+										const ws = workspaces.find((w) => w.id === e.target.value);
+										if (ws) setSelectedWorkspace(ws);
+									}}
+								>
+									<option value="">Choose a workspace...</option>
+									{workspaces.map((ws) => (
+										<option key={ws.id} value={ws.id}>
+											{ws.project_name} / {ws.repo_name} / {ws.name}
+										</option>
+									))}
+								</select>
+							</div>
+						) : (
+							<>
+								<div className="tool-starter-header">
+									<h4>
+										{selectedWorkspace.project_name} /{" "}
+										{selectedWorkspace.repo_name} / {selectedWorkspace.name}
+									</h4>
+									<button
+										className="ghost-button small"
+										onClick={() => setSelectedWorkspace(null)}
+										type="button"
+									>
+										Change
+									</button>
+								</div>
+								<ToolStarter
+									workspace={selectedWorkspace}
+									onStarted={handleClose}
+									onCancel={() => setSelectedWorkspace(null)}
+								/>
+							</>
+						)}
+					</div>
+				</div>
+			)}
+		</>
+	);
+}