All the "hardware wallet" implementations for Bitcoin show that you can make a secure element for BIP340 just fine.
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Ah yes correct.
BIP340 are Schnorr signatures?
From: https://trustedcomputinggroup.org/wp-content/uploads/TPM-Rev-2.0-Part-1-Architecture-01.07-2014-03-13.pdf
Section: C.4.3 EC Schnorr
"If a TPM supports ECC, it should support the TPM_ALG_ECSCHNORR scheme."