How to solve unable to activate Touch ID on this phone?

Make sure that you have the latest version of iOS or iPadOS. Make sure that your fingers and the Touch ID sensor are clean and dry. * For the Touch ID sensor, use a clean, lint-free cloth to wipe off any dirt or debris. Your finger should cover the Touch ID sensor completely, touching the surrounding metal ring.

If Touch ID isn't working on your iPhone or iPad - Apple Support

If you already tried (to no avail) all the steps provided in the support article that led you here, I suggest that you make an appointment (*) and have your device inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> Apple – Location Selector. After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.

Start by restarting your iPhone. After that, check if you have updated to the latest available software.

Check here: Settings > General > Software Update

See also this Support Article, for more information:

If Touch ID isn't working on your iPhone or iPad - Apple Support

How to update your iPhone:

Update your iPhone or iPad - Apple Support