Joshenlim/fe 4348 find an alternative to the jsr stdpath dependency (#50111)

## Context

Drops the `@std/path` dependency which is used in `EdgeFunctions.utils`
as `npm.jsr.io` was putting up a Cloudflare bot challenge on some
connections which blocks `pnpm install`. Instead, opting to directly
port the exact required methods as self-contained functions. Also added
some unit tests to check that UI behaviour remains status quo.

## To test: 
Important to test that everything in the edge functions UI remains
status quo
- [ ] Open an existing edge function with a single root-level file -
should load as expected
<img width="310" height="176" alt="image"
src="https://github.com/user-attachments/assets/4d724ab0-33bb-4093-a574-52984b2743fd"
/>
- [ ] Open (or create) an edge function with nested folders - confirm
file paths in the editor are shown correctly
  - Can create nested folders by using `../` as such
<img width="319" height="228" alt="image"
src="https://github.com/user-attachments/assets/dd345b1f-7c45-47e9-975c-f2f2e53a0106"
/>
- [ ] Similarly, download the edge function as ZIP to verify that the
nested folders are all correctly located
- [ ] Open a function with `import_map.json` - confirm still detected as
import map through the network tab GET request for the edge function
code (Examples here with and without import map)
<img width="333" height="245" alt="image"
src="https://github.com/user-attachments/assets/90fc90e3-4a62-493b-9246-ed7e3b662e96"
/>
<img width="290" height="237" alt="image"
src="https://github.com/user-attachments/assets/2f692362-c9d4-4394-bc5a-4f84ab5fb6f1"
/>
- [ ] Deploy a new function via the editor
- [ ] Update an existing function via the editor (Test adding new files
etc)


<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

- **Bug Fixes**
- Improved Edge Functions file path handling across supported
application environments.
- Nested entrypoints, URL-based entrypoints, root-level files, and
unmatched paths are now handled consistently.
- Generated files retain their content and receive sequential
identifiers reliably.
- Improved compatibility when processing and displaying files in
different application environments.

- **Tests**
- Added coverage for entrypoint path formatting, relative paths,
fallback behavior, unchanged paths, and identifier assignment.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

apps/studio/package.json

@@ -66,7 +66,6 @@
     "@sentry/react": "^10.27.0",
     "@sentry/tanstackstart-react": "catalog:",
     "@smithy/property-provider": "^4.0.4",
-    "@std/path": "npm:@jsr/std__path@^1.0.8",
     "@stripe/react-stripe-js": "6.1.0",
     "@stripe/stripe-js": "9.1.0",
     "@stripe/sync-engine": "1.0.32",