Amazing, thank you @ferdinand!
I figured GetActiveDocument() was the issue, so I was attempting to use takeData.GetCurrentTake() instead in the GetResolutionTakes callback but it still was exactly the same issue where the active take does not change. I didn't know about the callback data argument that already contains the correct document state in data[0], so thank you for letting me know to use that instead and pointing me to further details in the RegisterToken Documentation.
Replacing:
doc = c4d.documents.GetActiveDocument() with doc = data[0]
renderData = doc.GetRenderData(takeData) with renderData = data[1]
to get the following code below worked perfectly:
def GetCameraName(data):
	doc = data[0]
	bd = doc.GetRenderBaseDraw()
	sceneCam = bd.GetSceneCamera(doc)
	camName = sceneCam.GetName()
	return camName.upper()
def GetResolutionActive(data):
	renderData = data[1]
	renderResX = round(renderData[c4d.RDATA_XRES])
	if renderResX >= 1920:
		return "highRes"
	else:
		return "lowRes"
Thank you again very much for the help! Really appreciate it.