refactor: Restructure monorepo to apps/server/ and apps/web/ layout

Move src/ → apps/server/ and packages/web/ → apps/web/ to adopt
standard monorepo conventions (apps/ for runnable apps, packages/
for reusable libraries). Update all config files, shared package
imports, test fixtures, and documentation to reflect new paths.

Key fixes:
- Update workspace config to ["apps/*", "packages/*"]
- Update tsconfig.json rootDir/include for apps/server/
- Add apps/web/** to vitest exclude list
- Update drizzle.config.ts schema path
- Fix ensure-schema.ts migration path detection (3 levels up in dev,
  2 levels up in dist)
- Fix tests/integration/cli-server.test.ts import paths
- Update packages/shared imports to apps/server/ paths
- Update all docs/ files with new paths

apps/web/src/components/RegisterProjectDialog.tsx

@@ -0,0 +1,119 @@
+import { useEffect, useState } from "react";
+import {
+  Dialog,
+  DialogContent,
+  DialogDescription,
+  DialogFooter,
+  DialogHeader,
+  DialogTitle,
+} from "@/components/ui/dialog";
+import { Button } from "@/components/ui/button";
+import { Input } from "@/components/ui/input";
+import { Label } from "@/components/ui/label";
+import { toast } from "sonner";
+import { trpc } from "@/lib/trpc";
+
+interface RegisterProjectDialogProps {
+  open: boolean;
+  onOpenChange: (open: boolean) => void;
+}
+
+export function RegisterProjectDialog({
+  open,
+  onOpenChange,
+}: RegisterProjectDialogProps) {
+  const [name, setName] = useState("");
+  const [url, setUrl] = useState("");
+  const [defaultBranch, setDefaultBranch] = useState("main");
+  const [error, setError] = useState<string | null>(null);
+
+  const registerMutation = trpc.registerProject.useMutation({
+    onSuccess: () => {
+      onOpenChange(false);
+      toast.success("Project registered");
+    },
+    onError: (err) => {
+      setError(err.message);
+    },
+  });
+
+  useEffect(() => {
+    if (open) {
+      setName("");
+      setUrl("");
+      setDefaultBranch("main");
+      setError(null);
+    }
+  }, [open]);
+
+  function handleSubmit(e: React.FormEvent) {
+    e.preventDefault();
+    setError(null);
+    registerMutation.mutate({
+      name: name.trim(),
+      url: url.trim(),
+      defaultBranch: defaultBranch.trim() || undefined,
+    });
+  }
+
+  const canSubmit =
+    name.trim().length > 0 &&
+    url.trim().length > 0 &&
+    !registerMutation.isPending;
+
+  return (
+    <Dialog open={open} onOpenChange={onOpenChange}>
+      <DialogContent>
+        <DialogHeader>
+          <DialogTitle>Register Project</DialogTitle>
+          <DialogDescription>
+            Register a git repository as a project.
+          </DialogDescription>
+        </DialogHeader>
+        <form onSubmit={handleSubmit} className="space-y-4">
+          <div className="space-y-2">
+            <Label htmlFor="project-name">Name</Label>
+            <Input
+              id="project-name"
+              placeholder="e.g. my-app"
+              value={name}
+              onChange={(e) => setName(e.target.value)}
+              autoFocus
+            />
+          </div>
+          <div className="space-y-2">
+            <Label htmlFor="project-url">Repository URL</Label>
+            <Input
+              id="project-url"
+              placeholder="e.g. https://github.com/org/repo.git"
+              value={url}
+              onChange={(e) => setUrl(e.target.value)}
+            />
+          </div>
+          <div className="space-y-2">
+            <Label htmlFor="default-branch">Default Branch</Label>
+            <Input
+              id="default-branch"
+              placeholder="main"
+              value={defaultBranch}
+              onChange={(e) => setDefaultBranch(e.target.value)}
+            />
+          </div>
+          {error && <p className="text-sm text-destructive">{error}</p>}
+          <DialogFooter>
+            <Button
+              type="button"
+              variant="outline"
+              onClick={() => onOpenChange(false)}
+            >
+              Cancel
+            </Button>
+            <Button type="submit" disabled={!canSubmit}>
+              {registerMutation.isPending ? "Registering..." : "Register"}
+            </Button>
+          </DialogFooter>
+        </form>
+      </DialogContent>
+    </Dialog>
+  );
+}