So how are the systems isolated? If they are connected, what is so
special about entanglement?
...
But to my ears this just sounds like classical synchronization and a
measurement of noise level basically. What am I missing?
Try as I might, it is impossible to properly explain these questions in a single answer here. All I can do is give you some proper highlights, and let you study more from there. No one truly understands the inner workings (mechanism) of entanglement. Yes, it can sound "magical" and it is special indeed. So let's focus on the science, keep in mind I am presenting highlights related to your questions. :)
Usually, entangled pairs of photons (light particles) are created from PDC crystals driven by a laser. There is no further synchronization involved. Each pair emerges as a single system of N=2 quantum particles, sometimes called a "biphoton". This type of system maintains its original relationship even as the system expands. Yes, the individual photons do move away from each other separately in spacetime. But it is technically still one undivided system, not 2 isolated particles. You could say the particles remain "interconnected", except that there are no particular physics that explain how that works exactly.
Some of the rules around entanglement are well-known, even if the mechanism is not. In fact, even early quantum studies from 1935 featured discussions on this (resulting in the coining of the word "entanglement" that year). After both particles move away from each other, they are too far apart to maintain what you call a "classical" relationship. They instead manifest what is often called "quantum nonlocality", which indicates that lightspeed effects can no longer explain their behavior. (Some do not like this term.) So that nonlocality makes their ongoing state have the "magical" appearance, which is more or less unique in the quantum (and classical) world.
Eventually, both are measured in some way (for example, their polarization at various angles is observed). Once that happens, their entanglement ceases. But their entangled relationship displays a statistical dependence that cannot be explained by predetermination or hidden variables present from the moment of their original creation. The quantum predictions (confirmed by experiment) exhibit what are known as violation of Bell Inequalities. That's an entire subject of its own! I would not particularly call entanglement "fragile" either; entangled systems have been created and maintained in that state across a distance of over 1400 kilometers.
The paper below is a great reference that dives into the detail not possible for me to include here. That of course being in addition to the many lay summaries you can find online, although many of those tend to overemphasize the "magic" and under-present the vast experimental science in this interesting area of quantum mechanics. An oddity of entanglement not known to many: It is even possible to entangle different types of particles - such as 1 photon and 1 electron. So read up, it only gets more interesting!
Entangled photons, nonlocality and Bell inequalities in the undergraduate laboratory
Abstract: "We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric down conversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein-Podolsky-Rosen ``paradox,'' we demonstrate strong polarization correlations of the entangled photons. Bell's idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction."
