Keep media server up while maintaining the server

I have a Jellyfin instance with about 20 users. On weekends or in the evenings, I usually have 6 or 7 users using the server at the same time. These are also the times when I have free time to tinker with it. I now have plans to upgrade my server, which will take me at least 1 or 2 days (including 3D printing parts, trying them out, and optimizing said parts). The Jellyfin instance is running in Docker, with the media stored on my NAS.

My question is: is there any easy and straightforward way to keep the Jellyfin instance running without dealing with high availability, Kubernetes, etc., while maintaining the main server? I have my main PC and a couple of laptops I can use.