The real question is, if you have PayPal stablecoins, do you have the keys, or does PayPal? Can PayPal take your crypto money away or freeze it, as they routinely do with Paypal-controlled accounts? That's what really matters.
Of course self-custody is a bit misleading as they are any way IOU notes.
But this token does have code to freeze your balance of itself, an action controllable by the token contract administrators, which is Paypal.
this is seen in other similarly structured stablecoins.
but the fungibility of being an erc20 token means offloading it is very easy too, there would therefore be no limitations on transfer amounts, no delay in having liquidity based on the time of day or day of the week. No need to rely on Paypal’s interest in redeeming the token for cash again, as you could just swap them onchain for something else more liquid or more speculative the instant you wanted.
So at least it's honest.
> Although Paxos has the ability and the right to freeze all USD Stablecoins tokens
Yes Paypal can freeze PaypalUSD on an address level.