--snip--
I mean captcha like this,

I see, reCAPTCHA indeed is very annoying for Tor users.
I don't know exactly what you want, you ask question: how to check the balance for thousands of public addresses.
the loyce link only has data address which you can't check the address that you want.
There are 2 different type of file on LoyceV website, which are "List of all funded Bitcoin addresses
(sorted by balance (in satoshis), highest first)" (this is what @pbies use) and "List of all funded Bitcoin addresses
(balance not shown, sorted in alphabetical order)". I also tried download the former and can confirm the file contain balance in Satoshi unit.
$ head -n 5 blockchair_bitcoin_addresses_and_balance_March_01_2022.tsv
address balance
34xp4vRoCGJym3xR7yCVPFHoCNxv4Twseo 25259722706415
bc1qgdjqv0av3q56jvd82tkdjpy7gdp9ut8tlqmgrpmv24sq90ecnvqqjwvw97 16800998565493
1P5ZEDWTKTFGxQjZphgWPQUpe554WKDfHQ 12711157350542
3LYJfcfHPXYJreMsASk2jkn69LWEYKzexb 1166011365465
$ tail -n 5 blockchair_bitcoin_addresses_and_balance_March_01_2022.tsv
14jBn3YqcxFNtKmBXMHbC55Z5rsUDtTrrf 1
1JNuAjoN9cj8zyHfJ45nfhMMEgkoVwLvkT 1
1PiSSHEADZc72TzydsM98fXTizZ2HUdNJM 1
13xUr3oovz6rd2w9NrpHEyZfr1BfNs3pum 1
1JSU7TXuEqrEFD5aUr5BDs6yPBPW7THYkE 1