Some more thoughts :

If no such project exist yet, I thought it could work with an alternate,
small and fixed-length 'metric request block chain' of some sort.

It would temporarily stores structures defined as [metric request | current
block number when request was made | hash of the response] instead of
financial transactions.

These structures are verifiable so it could work the same way as a regular
financial blochchain.

It should not be part of the main Bitcoin protocol but could be a plugin
interacting with the data managed by the fullnode bitcoin software.

Also, metrics requests can be expensive to compute and validate, so it
would make sense to pay a fee everytime you ask one.

Does any of this makes any sense to you ?

Thanks,

Clément