BRIANiu ~ Battery Saver should not prevent a computer from waking up when a key is pressed, mouse moved, etc.
But, Windows Updates can change user settings, which it should never do.
chreid145 ~ In Device Manager, you can check to see if specific devices have the "Allow this device to wake the computer" turned on.
For example, click on "Mice and other pointing devices", then, right-click on one & click "Properties".
Check for a "Power Management" tab. If it doesn't exist, check the other devices listed.
On the "Power Management" tab, verify "Allow this device to wake the computer" is selected & "Allow the computer to turn off this device to save power" is deselected.
Ditto for Keyboard.
This may not solve your problem, but it is worth looking into.
Last year's (2019) Update KB4522355 completely destroyed my laptop & had to get a new one.
What I did notice before it completely died, was that there were a lot of 'Failure to Migrate' entries on the "Events" tab for many of the devices.
It should have been obvious to Microsoft that if you run into this issue while installing the Update, rollback & don't install this update.
But, it did not. It continued to install the rest of the Update. There were too many 'Failure to Migrate' entries for many devices to count.
This article doesn't directly address your issue, but it is one of countless articles on 2 specific updates (KB4532693 & KB4524244) that have created many severe problems on many computers with different hardware.
Microsoft confirms a known issue in Windows 10 KB4535996