Indeed, I agree that this would be the most likely concern. I have read through our HOA rules and there is no mention of bees. They mention limits on number of dogs/pets, and restrictions against farm animals. No mention of insects. I suppose an argument could be made that bees are farm animals, but I am willing so argue otherwise.
The HOA is a concern , thus my motivation to not have the hives in plain view from neighbors as they walk by. Our HOA doesn’t send around “patrol” cars looking for violations, but rather they respond to complaints. This is why I’m looking to be discreet. I seriously doubt that bee sting frequency will be increased, but the fear factor is very real for most people.
We aren’t permitted sheds either, but I could plant butterfly or other shrubs that could get tall enough to obscure site (and provide food).
In many areas, bees are considered livestock. So you likely are going to run into issues here. In my city I am allowed a limited number of hens, but all other livestock is banned (bees included). Most jurisdictions I see banning bees do so under a livestock ban, not a specific bee ban.
Regarding your pool, your pool is most like going to be full of bees, even if you provide a water source. The bees are attracted to strong smells and a pool smells just great to them (chlorine or salt water). I had a bee yard located out on a country lot, with several water sources in and around the yard, the neighbor 1/4 mile away through a small patch of woods had a pool. He claimed his pool was constantly covered in bees (which of course he was "allergic" to). The neighbor couldn't be reasoned with and rejected any compromise that involved the bees staying. The neverending harassment the landowner dealt with because of it (and threats of lawsuits) became to much for them to bear, despite being well within their legal right to have bees located on the property, and I had to relocate the whole yard on short notice. In our state hobby club, the question of "how do I keep bees out of my neighbors pool/hot tub?" is asked numerous times a year.
I perform dozens of cutouts (taking hives out of peoples structures) every year, and can tell you that any flying insect with stripes and a stinger is a "bee" to the average individual.
I wish you luck with your beekeeping endeavors, the first years are some of the hardest!