fix(ui): survive an unset BUN_PUBLIC_BASE_PATH in the browser

Bun inlines a literal `process.env.FOO` reference only when FOO is set. With
it unset — a bare `bun --hot src/index.ts`, which is what the README tells you
to run — the reference survived into the client bundle and the app died on
load with `ReferenceError: process is not defined`, before rendering anything.
Production builds were unaffected, because build.ts passes an explicit define.

Reading the value now goes through readBasePathEnv(), which catches. Catching
rather than a `typeof process` guard is deliberate: after inlining the literal
becomes a string, but a typeof test would still run in the browser and discard
that inlined value, silently breaking every subpath deploy. Verified all four
paths: dev unset (reference survives, caught, base "/"), dev set (inlined),
and root + subpath production builds (inlined by define).

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

src/ui/basePath.test.ts

@@ -1,5 +1,5 @@
 import { test, expect } from "bun:test";
-import { withBase, normalizeBase } from "./basePath.ts";
+import { withBase, normalizeBase, readBasePathEnv } from "./basePath.ts";
 
 test("normalizeBase defaults to root", () => {
   expect(normalizeBase(undefined)).toBe("/");
@@ -21,3 +21,18 @@ test("withBase joins without doubling slashes", () => {
   );
   expect(withBase("/sw.js", "/")).toBe("/sw.js");
 });
+
+// Regression: Bun only inlines `process.env.FOO` when the variable is SET. When
+// it is unset (e.g. a bare `bun --hot src/index.ts`), the reference survives
+// into the browser bundle and throws `ReferenceError: process is not defined`
+// before the app can boot. Reading the value must therefore tolerate `process`
+// not existing at all.
+test("reading the base path env does not throw when process is undefined", () => {
+  const saved = (globalThis as { process?: unknown }).process;
+  try {
+    delete (globalThis as { process?: unknown }).process;
+    expect(readBasePathEnv()).toBeUndefined();
+  } finally {
+    (globalThis as { process?: unknown }).process = saved;
+  }
+});