It depends, but also it probably doesn't matter.
For most of my RJ45, 10/100, or 100/1000 ethernets, I've connected the shield/chassis ground to my system ground using a 1M Ohm resistor and a 1nF capacitor, with a high voltage rating. I've got designs where I haven't or somewhere I've used a 10nF and I've never had an issue. The shield/GND connection isn't critical to the data.
This is typical stuff for a RJ45, this is a 10/100.
100/1000 with the magnetics built into the jack. A keepout as the jack manufacturer prescribed but that's it.
100/1000 with discrete magnetics
In neither of the above designs do I have anything more than a trace connecting the shield GND to GND, or the taps of magnetics. These designs were short cables to other equipment sharing a common power source, so no particular need to worry about chassis GND. I wouldn't say that this is canonically OK, and possibly there are standards/best practices I'm not aware of that might be relevant to your project, but I'm saying they all worked no problem.
For the first few designs I was extra cautious, with keep-out zones under the magnetics and RJ45, but these days I don't bother with them. I'd still respect no copper zones as specified by the manufacturer of the RJ45 but that's about it.
If you're going to use 1M Ohm / 1 nF, then your layout spacing doesn't really as much. The tiny amount of conductance/capacitance (in comparison) isn't going to have much of an impact on these values. There is some logic in keeping the chassis GND to one side as it might be noisy, particularly if you're ethernet shield is connected to a long where, or your connector shares the enclosure chassis GND, but then you can always connect the chassis to the system GND in a more suitable fashion elsewhere.
As far as chassis GND vs other signals, then again, if I had genuine reason to think that chassis GND was going to be full of noise then it might give it space, but it also depends on how vulnerable the other traces are. A relatively high impedance trace to my ADC, yep keep that away. LED outputs, run them as close as you like, even if the noise was so gargantuan as to affect them, it wouldn't really matter as much.
It only really matters in the context of your larger system, and what this is going to connect to. If you're using an unshielded cable, then do whatever, but if you're connected over a long cable run to a different building then maybe look up the standard. Your PCB layout, and the tiny amount of capacitance/conductance, isn't as critical though.
