Determine if angle is close to zero by +/- 2?

What you're doing works, but there is a way to do this in code that I suppose is a more direct/accurate code representation of the logic. That would be to check whether a range of values contains your value. In this case, we're checking whether the ranges 0 to 2 or 358 to 360 contain the relevant current angle in degrees.

As a side note, I like to wrap these sorts of calculations into my models as a computed property. It might look something like...

struct Angle {
    var degrees: Double

    var isCloseToZero: Bool {
        let upperRange = 358.0...360.0
        let lowerRange = 0.0...2.0
    
        return lowerRange.contains(degrees) || upperRange.contains(degrees)
    }
}

This can be accessed like...

let angle = Angle(degrees: 359)
let isClsoeToZero = angle.isCloseToZero

you could try the following code to achieve what you asked.

    var angle = Angle(degrees: 359.0) // Angle(degrees: 2.0)
    // between 358 and 360 inclusive or between 0 and +\- 2 inclusive
    if angle.degrees >= 358 && angle.degrees <= 360 ||
        angle.degrees >= 0 && angle.degrees <= 2 ||
        angle.degrees >= -2 && angle.degrees <= 0 {
        print("Yes, user is heading within a reasonable range from zero")
    }

Regarding CoreLocation course (heading), according to the docs, https://developer.apple.com/documentation/corelocation/cllocation/1423832-course

"... A negative value indicates that the course information is invalid..."

could there be a scenario where the CoreLocation heading is larger

I'm not sure, but lots of angle-related math might take your value out of the 0..<360 range. To remedy this, you can add make something like:

extension Angle {
    // Return a normalized copy of this angle that's guaranteed to be within +0 ..< +360
    var normalized: Angle {
        let potentiallyNegativeAngle = degrees.truncatingRemainder(dividingBy: 360.0)
        let positiveInRangeAngle = (potentiallyNegativeAngle + 360).truncatingRemainder(dividingBy: 360.0)
        return Angle(degrees: positiveInRangeAngle) }
}

Is there a built in method or better way to test for this?

No, but it can be pretty fun to write your own. Here's how I would do it:

// It astounds me that these basic operators aren't already built-in
extension Angle {
    static func + (minuend: Angle, subtrahend: Angle) -> Angle {
        Angle(radians: minuend.radians + subtrahend.radians)
    }
    
    static func - (minuend: Angle, subtrahend: Angle) -> Angle {
        Angle(radians: minuend.radians - subtrahend.radians)
    }
}

extension Angle {
    // There's probably some clever way to do this without branching,
    // and purely with modular arithmetic, but I couldn't figure it out
    func isWithin(_ delta: Angle, of target: Angle) -> Bool {
        return self.normalized > (target - delta).normalized ||
            self.normalized < (target + delta).normalized
    }
    
    func isCloseToZero(delta: Angle = Angle(degrees: 2.0)) -> Bool {
        isWithin(delta, of: Angle(degrees: 0))
    }
}

Here are some test cases:

print(" -340.0: ", Angle(degrees: -340.0).isCloseToZero()) // False
print(" -358.1: ", Angle(degrees: -358.1).isCloseToZero())
print("   -5.0: ", Angle(degrees:   -5.0).isCloseToZero()) // False
print("   -1.9: ", Angle(degrees:   -1.9).isCloseToZero())
print("    0.0: ", Angle(degrees:    0.0).isCloseToZero())
print("   +1.9: ", Angle(degrees:   +1.9).isCloseToZero())
print("   +5.0: ", Angle(degrees:   +5.0).isCloseToZero()) // False
print(" +358.1: ", Angle(degrees: +358.1).isCloseToZero())
print(" +360.0: ", Angle(degrees: +360.0).isCloseToZero())
print(" +365.0: ", Angle(degrees: +365.0).isCloseToZero()) // False

Here's a fancier variant, which does this totally branch-free using some clever modular arithmetic:

extension Angle {
    // Returns the distance between `self` and `target`, in the range `-180..<180` degrees
    func distance(to target: Angle) -> Angle {
        let rawDistance = (self - target).radians
        let normalizedDistance = .pi - abs(abs(rawDistance) - .pi)
        return Angle(radians: normalizedDistance)
    }
    
    func isWithin(_ delta: Angle, of target: Angle) -> Bool {
        let normalizedDelta = delta.normalized
        precondition(normalizedDelta.radians <= .pi,
            """
            `isWithin(_:of:)` always find the shortest distance between the two angles,
            so the delta has to be congruent to an angle between 0 and 180 degrees!
            It was \(delta), which normalized to: \(normalizedDelta)
            """
        )
        return abs(self.distance(to: target).radians) <= normalizedDelta.radians
    }
    
    func isCloseToZero(delta: Angle = Angle(degrees: 2.0)) -> Bool {
        isWithin(delta, of: Angle(degrees: 0))
    }
}