The latest news on this week's macOS updates is that the Mojave update to 10.14.6 appears as "secure" but the two security updates 2019-004 to Sierra and High Sierra remain inaccessible and should not It won't be attempted until Apple replaces them.
The problems appear to be in the BridgeOS update, which is specific to Macs with T1 or T2 chips. The version of BridgeOS or iBridge, 16.16.6568.0.0, provided with these updates seems to work properly in the 10.14.6 update, but may cause problems with sleep and alertness in Sierra and High Sierra Security Updates 2019-004.  At worst, this results in the updated Mac getting a core panic, either when trying to sleep or when it wakes up from sleep. Disabling system sleep is a solution for the time being, which is probably not too disturbing for desktop Macs. However, most users of MacBook Pro and MacBook Air models expect the computer to sleep when they close the lid and wake up when they open. If one of these actions causes the Mac to restart because of its core panic, this is extremely disturbing. The same basic solution can be used to turn off the Mac every time instead of letting it sleep.
If you have already used this update and suffer from these or similar issues, a potential solution is to upgrade to Mojave. Some users have reported that this is a reliable solution if you are ready to upgrade. You should also contact Apple Support, who may be able to provide further assistance and information.
Apple continues to make the Mojave update available, either through the software update pane, or for the standalone installers:
10.14.6 Combo update.
Currently, the two security updates are not available, and any attempt to install an old download should fail, as the Mac cannot get the BridgeOS update for it. Once these updates are available again, they should be back on:
High Sierra (2019-004)
So far I have not been able to find any information from Apple, but I am particularly grateful to Al Varnell and Mr. Macintosh for their help and information.
Last updated at 1525 UTC July 25, 2019.