I thought access to IMEI and IMSI was pretty heavily restricted starting with Android 10. Graphene [1] makes a few extra restrictions beyond AOSP [2], but it's been around for a while now.
To get access to IMEI and IMSI, you need to either be a carrier app, allowlisted, or grant the `READ_PRIVILEGED_PHONE_STATE` permission.
Unless Chrome is running at a system level in AOSP or some OEM specific firmware, I wouldn't expect it to have `READ_PRIVILEGED_PHONE_STATE`
The search engine has nothing to do with it.