what is the purpose of 'exist'?

You need to call 'Check item exists' before use 'On item exists'

Check item exists:

Check if a key exists in storage. This triggers either On item exists if the key exists, or On item missing if the key does not exist. If the item exists, the ItemValue expression is set to the key value in the On item exists trigger, so there is no need to use a subsequent Get item action to read the value.

On item exists

Triggered after the Check item exists action completes if the key checked does indeed exist. In this trigger the ItemValue expression is also set to the value of this key, so there is no need to use another Get item action to read it.

https://www.construct.net/en/make-games/manuals/construct-3/plugin-reference/local-storage

To add to the previous comment - you should not try to "get item" before checking if it exists.

On start of layout: Check if item "id" exists

On Item Exists: Set id to LocalStorage.itemValue