Bridges connecting Ethereum and Starknet will remain operational if Starknet transitions to an independent Layer 1 blockchain.

From the articleStarknet community overwhelmingly backs research into becoming an independent post-quantum Layer 1Also in Starknet Voters Back Post-Quantum L1 Research, Starknet's proposed Ethereum exit wins 93.52% support for further research, Starknet Votes to Explore Going Solo as a Post-Quantum L1, Starknet Voters Back Post-Quantum L1 Research, Starknet Moves Toward Post-Quantum Layer 1 as Voters Back Ethereum Split, Starknet Opens Layer 1 Research After 93.5% Poll Vote, Targets Quantum Safety by 2027 - Unchained