You have (or you could obtain) a QR code from your service provider. It will be easy to activate on a different device. The only point is you still have to contact your service provider because the eSIM must be deactivated on the previous device before switch to a new one
It doesn't have to be deactivated (well technically it's deactivated automatically on the provider side). Providers can transfer SIMs at any time between different SIMs, whether eSIM or physical SIM. If your provider wanted you to deactivate an eSIM then that's something that's not strictly required by all eSIMs and in general for all SIM cards.
For instance, people have been victims of SIM transfers in the US, basically a guy just walks into a carrier store, often bribes an employee, and without any security besides a fake ID gets the SIM of any customer transferred to a new SIM in store, no input from the old SIM required, the SIM is basically deactivated automatically upon the activation of the new SIM. It's the same for eSIM.
As that's a huge problem for security, they will understandably need some second factor to ensure it's the customer doing the transfer and not a criminal, so everyone (not just eSIM people) should have a PIN set on their cellular account, and then if you walk in with an ID you need the PIN to transfer. That's reasonable so make sure you know your PIN (or write it down somewhere safe).
Anyways, for eSIMs they present some complications over old SIMs. My provider lets me download an eSIM straight to any phone with their app. (I only know it's on iPhone currently, don't know about Android yet with my provider, but I know many providers don't have this functionality, Android does support it theoretically at least). To use an app though you need to sign in, and signing in means it needs a 2-factor code, which you can send to any phone line on your account, so either you need your old phone to receive a code, or you need another line of service (costs money) and you need access to know that code (you can have a partner or family member on your account receive codes, as long as you could call them you can get codes and sign in that way).
So that's kind of a problem if you're single and only one phone number on your account.
You can transfer eSIMs phone to phone, provider dependent as well, mine does have this, it's iPhone to iPhone but the iPhones have to be working, so not quite viable if your phone is broken and dead. Maybe if the screen is merely smashed but the phone still works you can work it just enough to get the eSIM transferred.
Basically if you have a broken phone you need to go to a store to get a QR code (and preemptively make sure you have a PIN set on your account and you have access to your PIN or you memorized it). And bring your photo ID. This is how carriers generally will work with eSIM. Many don't have electronic delivery features yet.
There's also another way to transfer eSIMs to a new iPhone as long as you have your Apple account signed in already, it's basically just loaded from the carrier directly. This is the "eSIM carrier activation" thing on this page:
https://support.apple.com/en-my/guide/iphone/iph3f11fba92/ios
Again, carrier dependent for carrier activation. This is how you buy an iPhone from the Apple store and it can be already activated the moment you pick it up at the Apple store, if you elect to activate it through your carrier.
All eSIMs only activate if you have Wifi on and connected. I had to learn that the hard way, I was in a carrier store, got the QR code and everything, but it wouldn't activate until I turned on wifi.
