Iphone 13 - charging only after a reboot

These are the only "software" troubleshooting steps you can perform:

A) Try a "forced" restart of your device using these instructions:--> Force restart iPhone – Apple Support

B) If the issue persists, something could have gone wrong during the latest update procedure.

I would try to install a fresh copy of iOS/iPadOS. To do this, create a full backup of your iPhone/iPad (1), then restore it to factory settings (you need a computer to perform this step) and, in the end, set it up as new (2).

When done, restore data from your previously made backup (3).

Follow the instructions provided in these support articles:

(1) How to back up your iPhone, iPad, and iPod touch – Apple Support

(2) Restore your iPhone, iPad, or iPod to factory settings – Apple Support

(3) Restore your iPhone, iPad, or iPod touch from a backup

If the issue still persists, contact Apple Support directly using this link:--> Get Support or, even better, 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.

If you already tried (to no avail) ALL the steps provided in the support article that led you here, take your device back to the service center (along with your charger and cable) and demosntrate your issue.

Regards

Giulio