Performance of bitwise operators on byte column vs individual bit columns
The answer to any performance question is "it depends."  Discrete columns can be fast and byte column flags can be fast too.  In absolute terms you can probably save a bitwise operation by having discrete columns here and there so discrete columns are theoretically faster.

A theoretical bump shouldn't be the main reason to choose a strategy. To paraphrase Jeff Atwood "storage is cheap and BDA's are expensive."  I would avoid the flags compressed into a byte column for the simple reason that it makes your life more complicated by making your data more cryptic.  Discrete columns will be straightforward to query, filter properly, debug, and pass on to future teammates.

For completeness there are other options than bit flags, or discrete columns.  One other option is the EAV (entity-attribute-value) model, even though it doesn't feel like this is your best option based on your description. 


  Entity–attribute–value model (EAV) is a data model to describe
  entities where the number of attributes (properties, parameters) that
  can be used to describe them is potentially vast, but the number that
  will actually apply to a given entity is relatively modest.