The update build numbered 23.5.A.0.570 is compatible with the LTE variant (SGP621, SGP641) as well as the Wi-Fi model (SGP611, SGP612). It brings forth Android 6.0.1 Marshmallow, which includes Doze, new app permissions, Google Now on Tap, a boatload of emoji and swathes of other enhancements as outlined here.
For now, it looks like Sony has completed its roll-out of Marshmallow to Xperia Z2 and Z3 devices. Dependent on your carrier, location or device's model number, though, the OTA may still continue to elude. Most of these updates are phased, so if you own a Z2 or Z3 and have yet to see any of Marshmallow, its arrival should be relatively close.
Have you gotten Marshmallow on your Z3 Tablet Compact or other Xperia device recently? Let us know how you're getting on with it via the comments.