Actually I don’t know why your CI run does not run with the stable release of Julia as well. It may be because of that Julia dependency. My package CIs always run on both.
Concerning the nightly build error, I had one experience with that and, at some point, I checked what was going on to see if that was something I had to solve or, perhaps, inform some other package developer. In my case, it was “my fault”, and the error would persist when the nightly build becomes stable.
Apparently they are passing in the Julia stable. You might do nothing and wait, or test the Julia nightly on your machine to localize the problem better and, perhaps, do something about it (as warning the developers of some package).
But, for example, you package will fail with that dependency on Julia 1.5 when the new stable version comes out, if someone tries to install it from Julia 1.6, and that might be the case of some package you depend upon. (Thus, it might be worth seeing if your package runs fine in Julia 1.0, if so, you can simplify your requirement to “1”, and you will be safe from your side until Julia 2).
No, I think it will run on 1.5.3 anyway if you put Jula = "1" as a requirement (you can test if you need 1.5 or greater in your machine, installing Julia 1.0 locally).
There may be some CI command to chose the Julia version (I don’t know). With the default CI file it seems that it will either run on the latest stable if that is compatible with your requirement, or will only run on the nightly build.