FYI: the only large stablecoin (AFAIK) that is different per chain is BUSD. The ETH version is issued by Paxos whereas the BNB version is wrapped BUSD on the ETH chain and then issued by Binance.
Maybe consider not only usdc but also other stablecoins. usdc is not as a sure bet as they portray themselves to be.
If you want to diversify, pick different stablecoins.