Do BIT columns offer any performance advantages for CCIs?
First, we are not comparing like data types.
Bit is defined as:

An integer data type that can take a value of 1, 0, or NULL.
BIT

Whereas BIGINT is a larger integer that consumes a significant amount of space by default.
That means by default SQL Server has statistics on each of the BIT columns and only one set for the BIGINT.
As you rightfully noted, BIT columns are optimized:

The SQL Server Database Engine optimizes storage of bit columns. If there are 8 or less bit columns in a table, the columns are stored as 1 byte. If there are from 9 up to 16 bit columns, the columns are stored as 2 bytes, and so on.
int, bigint, smallint, and tinyint

there must be a reason you are even considering taking at least 8 - 10 binary values and shoving them into a numerical number.
After all, why lot just use INT and save half the space? Since last I checked, 2,147,483,648 is 10 characters for just 4 bits and BIGINT has about 19, which technically is less space than BIT of youvspoit then into columns.
But this is losing sight of what your data is. How does BIT answer questions on what it represents? 10010 is just a number greater than ten thousand and yet in binary that actually represents something. If in &quot;Saving&quot; space you are forcing transformation before even using the data, will it still be efficient?
But please, do not conflate BIT with a numeric data type like Tinyint or BIGINT. They serve two different purposes.