In Drupal, you have a base-theme, and maybe a sub-theme. That sub-theme can also have another sub-theme.
Will Drupal be slower when using 3 themes, where each of them is a sub-theme of the previous one, or doesn't this affect the performance?
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TL;DR Have as many sub-themes as you want, it's not a problem.
Longer answer All types of inheritance, theming or otherwise, will have a performance penalty, and really all logic that you perform will have that effect; However
Generally speaking, I suggest you approach the problem the other way around. Organize your theme/solve your problem in a way that is efficient for you as a human. Then worry about how to make it efficient for a machine only when necessary.
Since your site isn't written in assembly, your entire site is a huge performance problem, but in the vast majority of cases, a cpu performing literally trillions of calculations in a second makes that a non-issue.