Chat Alert Sounds for members of different departments / for false departement

Description:

We have created two departments in omnichannel and assigned different agents to the departments accordingly. When integrating the live chat into the website, we used two different websites, on each of which we specified a department. Users should not be able to choose the department. Since they are already on the relevant website of the respective department.
Unfortunately, however, this leads to the following problem.
If we call up the live chat on the two websites, they are only ever assigned to one agent. This agent only has access to one of the two departments. The agent of the other department does not receive any requests.
Is there a possible setting that we have to set so that it is assigned to the correct agent? Or is it a bug?

Steps to reproduce:

1. Set up multiple Omnichannel departments with users in different departments
2. Open a chat for a user in department 1
3. Open a chat for a user in department 2
4. Agent A from department 1 will get audible two new chat ping
5. Agent B from depatment 2 don´t get a new chat

Expected behavior:

Agent A recieve chat for department 1 and Agent B recieve chat for department 2

Actual behavior:

Agent A get both chats, Agent B don´t get one chat.

Server Setup Information:

• Version of Rocket.Chat Server: 4.3.1
• Operating System: Ubuntu 20.04 LTS
• Deployment Method:
• Number of Running Instances: 1
• DB Replicaset Oplog:
• NodeJS Version: v12.22.1
• MongoDB Version: 4.2.17

Client Setup Information

• Desktop App or Browser Version: Chrome 98.0.4758.102 and Opera 83.0.4254.27
• Operating System: Windows 10

Additional context

Relevant logs:

No source file or test is named. Start by reproducing the issue with two Omnichannel departments and separate website department settings on the reported setup, then trace how chats are assigned to agents. Done means chats from each website reach only an agent in its configured department, with coverage for both departments.