Sensor.webhook_temperature: UndefinedError: 'dict object' has no attribute 'temperature'

Please edit your post and format your pasted config and data as per point 11 here.

Anyway, I pasted the json data you provided into the left side of this site: https://jsonpathfinder.com/

Then I had to replace all the fancy quotes “” with straight quotes "" in a text editor and try again (because you did not format your data as above).

Then I drilled down on the right hand side to obtain this path (at the top of the right hand side column):

x.event.data.temperature.value

So you need:

state: "{{ trigger.json.event.data.temperature['value'] }}"

The value on the end has to be in square bracket notation as that word has special meaning in templates (but you already had that bit sorted).