Yeah they are mostly Republic officers. One of my favorite little lines in Andor is when he says he's been fighting the Empire since he was 6. Palpatine established the Empire when Andor was a teenager, so he's saying he spent his childhood fighting the violent colonial extraction committed by the Republic.

Can you imagine any other star wars show talking about rebelling against the Republic? Incredible.

I believe the whole Imperial Navy got rapidly built up in about a decade after RotS, and it suffers from lowest-bidder mass production. Stormtroopers are shit conscripts because all the clones rapidly aged to death, TIE fighters are mostly cheapo bullshit with no shields. Rebel ships are a lot of legacy expensive hardware, and technology is pretty stagnant so they're just all around way better. The main part of the Empire rises and falls in less than 20 years, before being relegated to a few rump states that end up coming back in the new trilogy.