iPhone 13 not charging after software update

Did you try to force restart your device after the newest iOS update?

Force restart iPhone - Apple Support

Are you using the original USB cable and at least the Apple 20W power adapter?

Also check this article for more troubleshooting:

If your iPhone or iPod touch won't charge - Apple Support

If Optimised Charging is enabled, the iPhone will stop charging at a certain point and resume it later.

You can disable this option to rule out a software issue:

About Charge Limit and Optimized Battery Charging on iPhone - Apple Support

bea_03 wrote:

Did you mean that after every iPhone update I have to force restart?

At least a full restart is advised, yes

I'm not using the original Apple USB cable and adapter, but I don't think it's a cable problem,

Using third party cables can cause all sorts of problems.

Can you test original charging accessory, to rule out a hardware issue?

Is there anybody else using an iPhone who would let you try the charger?

You could also visit an Apple Authorised Service Provider nearby to do that:

Apple - Find Locations