set up next.js app and static build (#157)

This is a starter next.js app set up for static builds (static site
generation comes from output: 'export' in the next.config.ts). It uses
the 'use client' directive to tell Next.js to treat everything as client
side code in the page.tsx file meaning that most of the app won't be
prerendered. This mirrors our set up since we use MUI theming and CSS in
JS which require most of the app to be client code.

---------

Co-authored-by: Mark Kurtz <mark.j.kurtz@gmail.com>
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

Author: 3 people

.gitignore

@@ -178,3 +178,47 @@ cython_debug/
 # Project specific files
 *.json
 *.yaml
+
+
+# UI Section - Next.js/React application under src/ui/
+# dependencies
+/node_modules/
+/.pnp
+.pnp.*
+.yarn/*
+!.yarn/patches
+!.yarn/plugins
+!.yarn/releases
+!.yarn/versions
+
+# testing
+coverage/
+
+# next.js
+/src/ui/.next/
+/src/ui/out/
+
+# production
+build/
+
+# misc
+*.pem
+
+# debug
+npm-debug.log*
+yarn-debug.log*
+yarn-error.log*
+.pnpm-debug.log*
+
+# vercel
+src/ui/.vercel
+
+# typescript
+src/ui/*.tsbuildinfo
+src/ui/next-env.d.ts
+
+# Root-level UI config files that should be tracked
+!package.json
+!package-lock.json
+!.eslintrc.json
+!tsconfig.json