I want to be able to sit down and play a song from YouTube and then below it there would be a Spotify like card for lyrics or a searchable option like the one provided for local songs

Using Musixmatch, Lrclib, kugou, etc can be helpful.

Simpmusic does it well with their own local lyrics sharing solution. Maybe have a talk with him ?
Also the card doesn't look that pretty so maybe use the theming from spotify

Additional context
Screenshot of the app showing the synced lyrics card

Apps
Simpmusic

Thankyou to the developer for making such a beautiful online and offline music player. Salute 🫡