There is no privacy-focused PayPal alternative in the US, in part because US money transfer laws and policies (e.g. Know Your Customer) directly oppose privacy.

However, there are a couple of new projects that might eventually lead to something less bad for privacy than PayPal is:

• GNU Taler, if they ever get any exchanges, and they either figure out how to mitigate the high fees for wire transfers or use some other settlement method when people on different exchanges make small payments. (Their plan to use batch wire transfers won't help until the exchanges get a lot of adoption and frequent use. Of course, high fees discourage adoption and use, so this might not ever happen.)
• FedNow, if banks ever use it to offer appealing person-to-person payment services instead of just using it for themselves and their business customers.

Cash or Crypto is about all I can think of..

If your looking to move money from a bank to someone else's bank, I don't think you can expect to have much privacy in that from the parties actually making the transfer happen?

Monero?

https://www.privacyguides.org/en/advanced/payments/

Monero is the only privacy digital cash equivalent I'm aware of. There are a limited number of vendors who will accept it, and any of your friends who you can convince to take monero will also accept it

https://kycnot.me/?t=service

Here's a list of known services that accept it. Things like VPNs, web hosting, email hosting, game hosting, internet services basically

Any of the other payment systems, the bank systems like zelle, PayPal, etc ... They all have the problem of introducing a third party into your transactions. Who will then almost certainly sell your data

I'd bet you can guess why

If your use case is illegal and requires anonymity, digital money transactions are dangerous due to the US law requirements, even if the system is FOSS. Use cash or cryptocurrency with good opsec in such cases.

If money is involved there's most likely KYC so... no?