Thanks for the reply and the sources.

If I understood this correctly, I should rotate around x-axis first using alpha, then around y-axis using beta, and finally around z-axis using gamma angle. And I did that, and it appears to be quite similar to the ellipse I get in graphic tab of the project after the adjustment. So that seems fine.

Now, I have another question regarding about standard deviations of x, y and z for each point. If I draw them in CAD and overlap over my ellipses that I got as described above, I find them to be much showing much smaller area. Reading more in the documentation I saw that those standard deviations are about 20% of confidence in case of 3D points.
After a shorter googling I have found this

https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-statistics/h-how-directional-distribution-standard-deviationa.htm

And if I scale my standard deviations by the value of 5.20, I do get closer to the ellipse.

But it doesn't make much sense to me seeing that scale factor of 5.20 is for 3 sigma, and reading in the documentation it says that Šidak correction scales the deviations by a quantil from χ2_n distributon. So, I am wondering how do I find that scale factor exactly in order to have for example 95% confidence level? And do my standard deviations for x, y and z represent only 20% confidence level?

I am missing something here, but unsure what.