Hi Georgi we had the same issue. We were able to get something similar to work. We weren't able to use the OOO app at all as it would not meet our needs.

Here is what we ended up doing:

Create a custom user field checkbox - this is for Agents to click when they are OOO
We use a webhook to check the Assignee user fields to see if the checkbox is checked for every ticket created and updated
If it is, it adds a tag to the ticket and an autoresponder is sent out to the requester (the requester & CC's email option does not work as they have built in suppression rules)
Once message is sent, the tag that was originally added is removed so it can be checked again (an automation removes it after 24 hours so only one notification is sent every day)