We cannot use Embedded Chat Snippet code in the Salesforce Lightning components.

We can use Salesforce Visualforce page, Experience Cloud site, or in web property. Using Lightning Aura Component or Lightning Web Component will throw exceptions as the components wont be properly loaded on the browser.

Reference Article:

https://help.salesforce.com/s/articleView?id=sf.snapins_chat_limitations.htm&type=5

(You can’t add Embedded Chat to Lightning components. Use a Visualforce page, Experience site, or web property only.)