Is the esim really anonymous though? Your network provider does see the IMSI/IMEI right?
Discussion
You get an IMSI that's not connected to any identity. Once you connect it to a phone, it'll be transmitted together with your IMEI to the local network, if my understanding is correct. So you could be identified via your IMEI.
So for perfect privacy on that level, you'd need a phone (IMEI) that's not connected to your identity. I guess that's achievable if you buy a (used) phone for cash in a store.
If you want to dig deeper, Amir Taaki had a long thread on X on that topic a couple days ago, with very specific instructions on how to hack the IMEI.