What makes you think Google has access to your IMEI through using their search engine?
The search engine has nothing to do with it.
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`
[1] - https://grapheneos.org/faq#hardware-identifiers
[2] - https://source.android.com/docs/core/connect/device-identifi...