Custom Contact Panel in Salesforce

No, you cannot embed custom CCP (created using the blog you are referring) inside Salesforce.

If you are using Salesforce service cloud voice (SCV) then the contact panel that's used by agent is controlled by Salesforce team and you cannot replace it with a custom CCP. I will recommend to reach out to your Salesforce support team in this case.

If you are not using SCV and need a CCP embedded inside Salesforce, you can use Amazon Connect CTI Adapter. Refer https://github.com/amazon-connect/amazon-connect-salesforce-cti

The SF CTI adapter on SF AppExchange you are using is already a custom CCP that cannot be replaced.

So alternatively, you can take the same code to update agent's setting using Step function on a schedule basis to check all your agents (ListUsers and DescribeUsers) and see which one is using Deskphone mode and change it back. To search active users only if you have a lot, try using GetCurrentUserData with the filters that you need.