VPN, Google Chrome, and Torrenting

I’m hoping someone can provide clarity, or direct me to the correct information.

While using a VPN, does it matter if you are logged into google account in Chrome and proceed to torrent? The torrenting traffic will theoretically remain encrypted, but will Google retain records that I downloaded a torrent file from its browser?

What other steps should I take to protect my anonymity and privacy beyond throwing money at a VPN?

Shouldn’t matter because all it should do is download .torrent file, save it locally and then your associated torrent client opens it. (You can also use a magnet link offered by most trackers which you can just copy & paste.) Your browser doesn’t make any bittorrent peer connections.

What other steps should I take to protect my anonymity and privacy beyond throwing money at a VPN?

Chrome is not a privacy-respecting browser because of the tracking & analytics it is running under the hood. If you want to keep Chrome’s best part (rendering engine), use some other Chromium-based version like vanilla Chromium (still has some google stuff), ungoogled-chromium or Brave Browser.

Where do you find ungoogled Chromium?

Vouch for Brave- it’s a nice browser