It's been years since I played the stock game, but as I recall, the only promotion that matters in terms of improving crewman stats is from Seaman 1st to Petty Officer.
I'm playing FotRSU and I just verified that promoting seaman 2nd and Seaman 3rds don't change their stats at all.
Promoting a Seaman 1st to Petty Officer with a specialization in Torpedoes gave him +40 to Leadership, +20 to Mechanical and +20 to Weapons.
The list is as follows
Command +40 Leadership +10 Electrical +20 Watch
Engines +40 Leadership +20 Electrical +20 Mechanical
Guns +40 Leadership +10 Mechanical +20 Guns +10 Watch
Sensors +40 Leadership +20 Electrical +20 Watch
Torpedoes +40 Leadership +20 Mechanical +20 Guns
Watch +40 Leadership +10 Mechanical +10 Guns +20 Watch
That's based on the table here
https://silenthunter.fandom.com/wiki/SH4_Crew_Management§ion=2
I'm pretty sure that the promotions in FotRSU work the same as in the base game.
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