What is the standard way to generate a unique non-reproducible ID?
It is desired a Unique Non-Reproducible ID (UNRID) which genuineness is publicly verifiable.

I know no standard for that. But we can take as UNRID the signature of a public fixed message (e.g. empty), if the signature scheme is randomized and EUF-CMA secure. Verification simply checks the signature. If probability of collision among signatures is satisfactorily low, security follows from EUF-CMA.

The signature scheme could be RSASSA-PSS of PKCS#1v2.2, with the advantage of fast signature verification. But for modern security that requires 256 bytes (342 Base64 characters), which is a lot.

A more compact option is a slight variant of ECDSA, where a signature $(r,s)$ becomes the UNRID $(r,\min(s,n-s))$, which is presented as EUF-CMA secure there, without proof but plausibly: EUF-CMA security of the signature scheme matters in Bitcoin, and was repaired with apparent success, in a manner equivalent to what's proposed. That would make the UNRID 64-byte (86 Base64 characters).

Using a signature scheme with message recovery, we can embed a serial number or other small ancillary information in the UNRID, without making it bigger. For RSA, ISO/IEC&nbsp;9796-2 Scheme 2 would do (it's essentially RSASSA-PSS with message recovery). There are ECC-based randomized signature schemes with message recovery as compact as ECDSA, see bibliography.