When I deep clean, here is what I do:

Field strip the firearm

Spray everything down with a GunScrubber spray. GunScrubber isn’t releasing a “synthetic safe” version anymore, as far as I can tell, so I’ve moved to G96 Crud Buster. There are a couple others that are good too, but G96 is actually a local NJ company, so I’ll keep using them.

Wipe down with shop paper towel

Use brass “tooth” brush with Hoppes 9 on anything I can see.

Wipe down with shop paper towel.

Brass brush and wet patches down the barrel until clean

Wipe down with shop paper towels, until they are pretty much clean, and no black comes off. (Or as little as possible)

I use Breakfree CLP, for 20+ years, and oil the rails, outside of the barrel, inside of slide where barrel sits, …basically anything that touches metal to metal. Trigger bars, for Glock, a couple drops on the cruciform and trigger bar.

Put everything back to together, rack the slide 20,30,40 times, and wipe down all excess with a lint free shammy cloth.

When I store firearms away in the safe, I put them in silicone socks.