I recreated the databricks (there's no other way to solve that). If it was a production databricks workspace it was a disaster!
I have created a VM with static public IP and added this IP to the IP access list. Hopefully it'll become the last resort in case all other IPs will be replaced.
The above is an ugly workarround. No matter where I have looked, the only solution is to have private endpoint which requires other resources (peered VET + VPN) that I do not want to get into in this project.

As for the original issue, the issue, as mentioned above, was the SQL warehouse that couldn't start. I have created a new serverless SQL warehouse and added it to the job instead of the starter warehouse that was available and problem solved