Another option is to use crypto portfolio tracking apps, such as Delta App, CoinStats, CoinTracking, Blockfolio, Coinigy, etc.
The problem with this suggestion is the same as the problem with the other suggestions made above such as a blockchain explorer or Google sheets, as you rightly point out - privacy. As the old saying goes, if you are getting something for free, then you are the product. These services are almost certainly harvesting your data and sharing and selling that with third parties. Setting up an Electrum watch only wallet synced via your own node avoids all this.
If you do want to use a crypto portfolio app, then I would suggest manually entering aggregated balances rather than linking it with your wallet or specific transactions, so it cannot track your specific coins.
Would it make sense to use listunspent[1] afterwards? This would allow the OP to get the current balance of each address, albeit it wouldn't provide him with a total sum. Is there any command that he could use in CLI to sum each value from the provided addresses and spit the result at the end?
He can use the command
listaddresses(balance=True) to get a list of all addresses alongside their individual balance, or the command
getbalance() to get a total wallet balance.
The reason I suggested just doing
listaddresses() on its own is because even if he imports a bunch of empty addresses, it means his watch only wallet will automatically stay synced with all this other wallets as he uses more addresses (until he exceeds the gap limit on a wallet, in which case he will need to import the next set of addresses).
OP: In order to achieve a better degree of privacy, I would recommend you to run your own node and then you could retrieve this information without relying on any external entity by using Bitcoin Core CLI.
I obviously agree as discussed above, but actually if OP is going to be running his own node anyway, then he could avoid the Electrum watch only wallet and simply use Core, importing the master public key from each of his Electrum wallets in to a single Bitcoin Core descriptor wallet.