I just bought a 2019 Giant Defy Advanced 2, with Giant's "Conduct SL Disc" brake system and it's the only thing about the bike I don't like, for many reasons. But my question is, are the rotor mount holes "universal" i.e. can I replace the Giant system with Shimano 105 mechanical brakes? Any help would be greatly appreciated.
There are two standards to mount disc brake calipers that are relevant to you:
Have a look at Nathan Knudson's explanation to identify what your bike has. Its specs sheet might also help.
These are industry wide standards. A Shimano flat mount will fit, for example, on a bike that came with SRAM flat mount.
There are adapters for flat to post mount available. However, it is better to avoid these. In particular post mount calipers on flat mount frames are quite a bodge.
All rotors and calipers are cross compatible (at least all that are relevant to your case). It will be enough to align the new calipers for existing rotors. However, one needs to check brake pad compatibility. Some (mostly very cheap) rotors must not be used with sintered pads.
The Conduct Sl system allows Giant to use mechanical disc brake shifter/brake units with hydraulic calipers.
If you want to swap out to 'proper' 105 hydraulic you'll need new shifter/brake units, lines and calipers, a stem and maybe rotors. That's not inexpensive. If you wanted a fill 105 Hydro setup ideally your would have bought a slightly higher Defy model with 105 hydraulic already installed - but presumably you did not realize you didn't like the Conduct system until later. If you have done minimal miles on the bike you might want to return to the store and ask if you can upgrade - that might be cheaper than the new parts and installation.
Answering you compatibility questions: the rotors are standard 6-bolt mounting. you might need to swap them for rotors compatible with 105 calipers, I'm not sure about that. The Conduct calipers are standard flat-mount type so 105 flat mount calipers will bolt right on.
FYI I believe Giant sells a computer and light mounting adapter that works with the Conduct stem and head unit, if that helps.