My Apple ID associated with my new phone is currently compromised

The IMEI gets broadcast openly over the phone network. The IMEI is rather removed from what you will want to be concentrating on protecting and updating and securing here. A whole lot more trouble can arise with compromised passwords and accounts. Your Apple ID can be used to remotely wipe and lock your device, for instance. An IMEI, not so much. The IMEI is akin to the Ethernet or Wi-Fi MAC address. It’s not really a secret.

If you specified encryption and provided a secure password and din’t save the password in keychain on the target system, the backups are inaccessible.

If you did not specify an encryption password or used a weak or known password or allowed the password to,save in Keychain on the backup system, not so good.

If your backups were exposed... Change your Apple ID password, change all passwords to new and unique values, passwords including those on your primary and recovery email accounts, enable two-factor authentication, log out all unrecognized or untrusted devices from iCloud, and otherwise assume compromise. Painful as all these changes are, yes. Check your Apple ID trusted telephone numbers and trusted email and trusted devices, too.

IMEI is not security relevant. Your passwords and the rest are.

If you think your Apple ID has been compromised - Apple Support

We'd need a bit more information:

how is it "compromised"? And what happened to get to that point?

IMEIs are not hard to get and there is not inherit benefit to someone else having it. It does not allow them to compromise your phone.