I've never quite understood why people use a random website to check if their own transaction has confirmed. Once you've broadcast your transaction you can just monitor its progress through your wallet. Opening up a block explorer and continually refreshing a specific transaction is pretty much a guarantee to the block explorer that you made that transaction, and they can link your transactions and addresses to your IP, your browser fingerprint, and other information about you. The same is true of third parties like Cloudflare or Captcha services.

For what it's worth, Blockchair probably have the best Privacy Policy of any block explorer, which you can read here: https://blockchair.com/privacy.

I still wouldn't advocate for trusting any third party with your privacy, though. If you are going to look up transactions on a block explorer, use Tor.