There are certainly parts which are specific to certain brands of frames, and to specific models too. Examples:
- Aero seat posts. Being non-round, they could be any weird shape, which has aerodynamic advantages, but also lets the frame maker copyright their profile, so that there are no cheaper alternatives.
- Integrated stem/bar combinations - same as seat posts
- Hangers - every other frame seems to have its own special hanger setup. There are manufacturers of aftermarket hangers.
- Odd little covers, to match Di2 holes or similar. These tend to be too small and low profit for aftermarket makers to bother with, so original tends to be the only option.
While there are special designs for saddle mounts, the vast majority of them are the standard two-rail design. The rails are almost always 7mm in diameter whether they're made of steel or carbon fibre.
However some saddles come with 8mm or 9mm round rails, or 7x9 or 7x10mm oval rails. These tend to be expensive MTBs. Some older saddle designs have four rails (eg, some Brooks leather saddles)
Here's a single-rail I-beam - again super-expensive bikes:
And there are doubtless custom-proprietary saddle mount systems too - I'd suspect expensive Tri bikes have a range of mounts.
Upshot: your bike has a normal dual rail system, on a normal two piece, two-bolt clamp. Back off the two visible hex-bolts, remove saddle, and fit the new one. The hardest thing is finding one to buy that you find comfortable, and then dialing it in just right can take time to get perfect. But its eminently do-able.
Any LBS can help you out, or buy online. You do not need to buy a branded bike saddle from the maker of your bike.