A precursory google tells me you should be able to customise cursors on linux using .cur files, so you should be able to use these on Linux - I can't test it myself though.
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linux doesn't support 'ani' and 'cur', but to be absolutely sure i tried it and it didn't work, i've also done some research and there is a way to convert them but it is a pretty tedious process and isn't noob friendly, beside not even being a perfect solution since it only converts for the X11 display protocol and not Wayland, since you don't use linux yourself and can't test, it's a shame you won't make them
What kind of file type do you need? Searching on google isn’t giving me a clear answer but I’m happy to help if I can. If it’s more complicated than converting to a file type I might not be able to do it, I just made these on an art programme that allows saving as .cur files and I have very little programming experience. It’s not that I ‘won’t’ make them, I would love to make them as available as possible, it’s just that I don’t know how and from what you have said I suspect it may be beyond my ability, sorry T_T - that being said, the .cur image files are freely available to be edited and manipulated however you like for personal use. I know some people use browser extensions to use them just when surfing the web, a more limited use but this could be an option for you.