I think you're using the formula
(360)/(4*1024) because of the term quad in quadrature encoder, but a quadrature encoder doesn't have anything to do with four, it's from the the use of the term to mean two signals that are offset by 90 degrees.
Your quadrature encoder will have TWO encoder rings (not four), and the resolution is 1024, not some multiple of it. What you'll wind up with are two channels, typically
B, with each encoder wheel being 512 counts per revolution, and then the wheels are aligned in quadrature, meaning they're offset by 90 degrees.
If I use
a to mean channel A is low, and
A to mean it's high, and
B similarly, then you'll get the following readings:
They're not in phase, or it'd go
AB, and they're not 180 degrees out of phase, or it'd go
Ab. Only when they're 90 (or 270!) degrees out of phase do you get that sequencing. In the example above, A is leading B - on one step A toggles, then on the next step B transitions to the same state as A.
If the encoder is moving in reverse, then A will follow B, like:
And so you can get both position and direction by monitoring the encoder counts. Here's a handy graphic from the Wikipedia entry on quadrature encoders:
And so finally, to answer your question, the actual encoder resolution isn't
360/1024 = 0.3516 deg. The maximum angle error is very close to (but less than!) this resolution, but I typically would expect anything within +/- the least significant bit to be noise, so it's not a huge deal.
The terminology in the encoder documentation is very confusing, notably the "bar and window" and "electrical degrees," so I looked for the "bar and window" term and found the following graphic from another encoder manual:
Apparently the "bar and window" refers to the dark and light bands on the encoder wheel. In OP's snippet from the manual:
1 Cycle = 360 electrical degrees
= 1 bar and window pair
I can only assume they're calling them "electrical degrees" to refer to the cyclical nature of an encoder output, which should be
0011 0011 0011, etc. Each "cycle" is "360 electrical degrees" in that, after a full "cycle," the encoder is back to the initial state. This meshes with the concept of a "state width" in "electrical degrees," where
State Width: The number of electrical degrees between a transition in the output of channel A and the neighboring transition in the output of channel B. There are 4 states per cycle, each nominally 90°e.
Further, if the snippet defines Count as:
Count (N) = The number of bar and window pairs or counts per revolution of the codewheel
then as I mention above, if the inner ring has 512 "bar and window pairs," and the outer ring has another 512 pairs, then there are 1024 pairs in total.
I personally think the whole concept of "electrical degrees" is whack and I'd probably prefer to call them encoder transitions or state transitions, but that's just a personal preference.