What privacy benefits am I forfeiting by running my Bitcoin over clearnet instead of Tor?

Long time accumulator (2015) and fan, first time poster.

I downloaded and installed Bitcoin Core on an AWS server today. At the current rate, it'll take me twenty-five hours to get sync'd up.

I'd like to understand the privacy vulnerabilities implied by running the full node on clearnet instead of behind Tor. I've googled but am getting some conflicting information.

• Presumably anyone who probes my AWS public IP will see port 8333 is open. They'll know a Bitcoin node lives there. That doesn't particularly bother me; It's not illegal to run a node.
• Of greater concern is having an outbound transaction tied back to me. If I relay a TX through my node, is there any way to prove that particular transaction is tied to a private key owned by me? I mean, as a full node operator, tons of transactions will be relayed through there, yeah? Seems like my own transaction would just be one of many. There's no special flag in the protocol indicating that I originated it, correct?

What're the downsides (if any) of running Bitcoin Core over Tor? Tor looks incredibly easy to configure, yet most nodes are on clearnet, and I'm wondering if there's a reason for that.