Do eSIMs have any downsides from a privacy standpoint?

Compared to regular SIM cards.

SIMs are easier to swap if needing to switch phone, but I only see this as a convenience. I don’t see why it would be more private.

I have little knowledge on how eSIMs work, but something in the back of my mind, tells me that somehow, eSIMs are bad for privacy :(

Anybody care to share their views on this?