Sub-issue of #677

With the migration to chain_index backend complete, the old local_cache module is no longer used and should be removed. This includes:

• The local_cache module itself with its finalized and non-finalized state implementations
• The associated integration tests that tested the old caching mechanism
• Any leftover imports and references throughout the codebase

Removing this dead code will reduce maintenance burden and make the codebase cleaner.