The interview process lasted for a while, it was a month and a half from the start of the communication to getting an offer.
The process had several rounds, in this order:
Beginning interview (30ish minutes)
Task (1 week)
Technical interview (1h30min)
HR interview (about 2 hours)
visit to Ljubljana - VP interview (2x30 min)
In the beginning interview, I got to know the head of the department and got a more in-depth overview of responsibilities for the future role. The head asked me am I willing to relocate, and is the expected salary range. The expertise test was sent to me minutes after completing the first interview.
The expertise test - had two tasks which pretty much are standard for game design tests - understanding players' motivation, user segments, wanted game experience, and then using that knowledge for analysing and making a minigame which would be interesting to the target audience. :) Deliverables were a GDD written in a way as if the game was presented to the rest of the team, and a document with an analysis of two games' and twisting one of them to fit the target audience's needs. The time given for the task was enough to complete the task without a great amount of stress.
I got a suggestion to play as much games from the brand universe as I can, and connect and compare to the similar stuff I've been working on so far. Technical interview was held by the head of the department and a senior game designer, and consisted of roasting the less polished parts of the design from the previous task, aka feedback. :D The point of this part was understanding the thought process behind the design, seeing what could be improved and if you understand pros and cons of your design, seeing how you react to feedback, and general awareness of the brand's needs and future.
HR interview was a culture fit one, basically google "hr interview questions" or "how to prepare for a culture fit interview" and you are good to go, so I don't parrot already existing (and more concisely written) sources. I cannot overstate the importance of preparing for each stage enough!
The last part was a three day visit to Ljubljana, meeting the team in both an informal and formal environment. I got the chance to see a bit of how an actual workday looks like, and it helped me arrange the puzzle and ultimately "sold" me the team. :D Two days were informal, and one day was a work day. During the work day, I had two more interviews with two different VPs, and got to ask the questions at a brand and culture scale. Everyone in this process (including the VPs) was incredibly kind and approachable!