The home button doesn’t see my fingerprint

Follow the instructions here, If Touch ID isn't working on your iPhone or iPad - Apple Support If that does not work, then use the link in the support document to contact Apple Support for assistance.

Sometimes, it is possible to damage your fingerprints such that they are not recognised by the TouchID sensor. In such situations, it is necessary to re-register your fingerprints.

For example, today I myself have had to re-register my own fingerprints on my iPad and iPhone. Having spent much of the day cleaning my cars, using old-fashioned contact-cleaning with a bucket and sponge, my devices found my fingerprints to be unreadable. After registering fresh fingerprints, normal service has been resumed.

In conclusion, your problem may not be with your device(s). Before seeking a more technical cause or issue, perhaps try re-registering your fingerprint(s).