If websites can't trust that their users are authentic they will probably institute even more intrusive checks.
I haven't been optimistic about the future of technology for a while now. :'(
Essentially, the manufacturer of the device + operating system will generate a unique signature per each device, and web browsers will be able to access it.
From what I understood, each TPM has a unique private/public key pair (Endorsement Key (EK)), and then this key is certified by the manufacturer of the TPM.
From there, you can generate a Attestation Keys, and these keys are signed by the EK.
https://security.stackexchange.com/questions/235148/whats-th...
So essentially, at the end of the day, Chromium would ask the TPM for attestation, and it would act as a unique Device ID.
Then they can allow only a selected list of TPM manufacturers certificates, to prevent emulators for example.
TL;DR: Chromium on Linux would ask the TPM chip for a signature, and each TPM chip has a different signature from the moment it is out of the factory.