Hello. What a gorgeous haven you have there. Despite the beauty, I'd be mad as a hatter with the contractors though, because i feel you've been set up to fail here.
To preserve the beautiful work and come up with an effective solution I strongly recommend hiring a hydrogeologist to engineer your drainage plan. The layout is not straightforward to my mind. While the words "hydrogeologist" and "engineer" sound expensive, I'm not sure they have to be. In my neck of the woods I don't think I spent more than $500 on a consult, but I learned a lot. I'd hired mine to assess whether or not the foreclosure I was buying on the side of a hill with a river at the bottom and a pool where the former catch basin was was "sound" or not in terms of drainage.
As it turned out, it was sound, so I'll share what was done on construction, recreated from the info we'd gathered before we were comfortable making the purchase (its a vinyl pool, so we were especially concerned about liner float and soil erosion ergo concrete surround movement.)
A trench had been dug all the way around the pool (after the concrete area that on two sides is fairly narrow) and topped with decorative 2-3" stone -- large enough not to be problematic if it got in the pool during leaf blowing, etc.
You don't have to use stone, though it would look nice in your setting. The make a perimeter drain grate for pools that need this type of protection. I'll try to find you a link.
My perimeter drainage the connects with two large underground drains on either side of the house that run all the way to the road. All my eaves are also connected to the underground system.
The side of the hill before the pool was terraced down two levels, draining to the perimeter drain. Note that while I do mulch the terrace, I've also heavily planted it beyond original owners to prevent soil erosion and excess runoff. Ground cover is especially useful for this. In your case, ground cover over decorative stone would be a good idea for your beds. Not sure in your climate, but creeping thyme, periwinkle, etc. would be lovely. Native grasses also help when there are drainage issues.
I'd need to look at your pond more closely, but am thinking some kind of breach berm between its pool-side edge might also prove useful.
In my case, and unlikely necessary in yours, there was also a sump created below my deep end, plumbed to my pump so I could close the other valves and either pump it to waste or send the water to the pool in heavy rain events...there's gravel in the sump and the water seems pretty clean the few times I do that in spring.
The only thing with long runs of drains is every so many years you may have to jet them if debris builds up. But in my case were talking about runs a few hundred feet long because I'm on a 2+ acres lot.
Hope that helps give you some ideas for a retrofit. Here's a quick link to pool trench decorative drains, but search around to see what all is possible. This will get you started:
Trench Drain Systems | Pool Trench Drains
. I used to love doing that! I'd actually love to do it right now!
