refactor(api): replace plex-api package with internal implementation (#2335)

Removes plex-api dependency and its type declarations. Then extends the ExternalApi class for
PlexAPI implementation to mimick the exact same old behaviour. This should resolve the security
vulnerabilities in transitive dependencies: form-data(critical), request (moderate, deprecated),
tough-cookie (moderate), xml2js (moderate). Plex-api itself is also no longer maintained.

package.json

@@ -76,7 +76,6 @@
     "nodemailer": "6.10.0",
     "openpgp": "6.3.0",
     "pg": "8.16.3",
-    "plex-api": "5.3.2",
     "pug": "3.0.3",
     "react": "^18.3.1",
     "react-ace": "10.1.0",