This is the exact correspondence between military ranks and civil service grades

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Chairman of the Joint Chiefs of Staff = Minister level
General (4-star) = Vice Minister level
Lieutenant General (3-star) = Grade 1
Major General (2-star) = Grade 2
Brigadier General (1-star) = Grade 3
Colonel = Grade 4
Lieutenant Colonel = Grade 5
Major = Grade 6
Captain = Grade 7
First Lieutenant = Grade 8
Second Lieutenant = Grade 9 (Academy graduates are Grade 8)
Sergeant Major / Warrant Officer = Grade 7
Master Sergeant = Grade 8
Sergeant First Class = Grade 9
Staff Sergeant = Outside the grade system
You can consider this to be the practical perception.
Since there is virtually no barrier to entry for a Staff Sergeant,
to be honest, they aren't really treated as civil servants at all,
whereas a Second Lieutenant is a college graduate, so they are treated like a Grade 9.
The rumors about them being treated as Grade 7 are honestly far from the truth.
Second Lieutenants from military academies are guaranteed to reach Grade 5 in the future, so they are viewed as Grade 8.
A Colonel receives protocol similar to a Police Chief at local events,
and at the Ministry of National Defense, they are treated as Grade 4, so this is accurate.
Regarding Generals, it is correct that only the Chairman of the Joint Chiefs of Staff is at the Minister level.
Looking at the treatment of a General's aides, they are treated at the level of aides to Vice Minister-level officials,
but only the Chairman of the Joint Chiefs of Staff's aides receive special treatment, one grade higher than other Generals' aides.