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• The postfix AtIndex is too verbose. You don't have any other operations like AtMask or anything and the index is provided as argument. So I would prefer IsBitSet over IsBitSetAtIndex etc.
• The index is sometimes a byte, sometimes a uint. I would not bother with such level of (over-)engineered type picks. Stick with the common type for an index int. You can always add argument checks for bounds.
• You can replace 1 << 7 - index with 1 << index in your operations. This is written more compactly and is a well known bit operation technique.