Updates If you are already subscribed to /v2/updates and storing the results, then yes, you could use that for summing the amount of holdings.
PQS The Participant Query Store copies updates into a Postgres database. You can then write SQL queries to get all kinds of information, including balances.
Active Contracts In the general case, you can use the /v2/state/active-contracts endpoint to get the UTXO holdings for a party. And then sum. (If you are using the TypeScript Wallet API, there is a function specifically for getting the collection of CIP-56 holdings.)
Canton Coin For CC specifically, the Scan Aggregates API provides a v0/holdings/summary endpoint.