My MacBook Air will force shut down programs when the display goes to sleep

It is probably a Kernel Panic that happens when put it to sleep and computer restarts bringing you to the login page that requires password instead of Touch ID. If you have not done so already, always start with a Safe Boot to check if that solves the problem. How to use safe mode on your Mac - Apple Support

I would also suggest posting an EtreCheck report that allows Full Disk Access. EtreCheck is a common diagnostic tool used here that is safe and does not provide personal identifier information in the report. To post it here, you will have to choose the "Additional Text" option.

I don't see any of the usual suspects in the report. However, I noticed that you don't have Time Machine enabled with backups. That should be the first and foremost thing to do: get a full an current backup of your boot drive whether it be with Time Machine, Carbon Copy Cloner or ???.

Here's some food for thought. Unless you're using a true VPN tunnel, such as between you and your employer's, school's or bank's servers, they provide false security from a privacy standpoint.  Read these two articles: Public VPN's are anything but private and Former Malware Distributor Kape Technologies Now Owns ExpressVPN, CyberGhost, Private Internet Access, Zenmate, and a Collection of VPN “Review” Websites. 

You have a large number of apps crashing. I would remove all items from the System/General/Login Items setting pane, both at the top of the pane and below. Then boot into Safe Mode according to How to use safe mode on your Mac and test. Then reboot normally and test again. Run for a while to see if the apps shutdown during sleep or not. If not then add them back one at a time and test.

Note:  if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode.  This makes it act as a wired keyboard as will assure a successful boot into Safe Mode.

If you still experience apps shutting down after sleep with no additional apps open via the Login Items it will be time to make an appointment at the nearest  Apple Genius Bar or Apple Authorized Service Provider.  

Since the problem goes away when booted into Safe Mode, you should look more closely at the apps that run on startup and in the background at  > General > Login Items.

It also appears there are a few Extensions installed in Safari. Disable these at Safari > Settings > Extensions.

Some of the apps that need to be checked are:

• OpenVPN
• TickTick App/Widget/Plugin
• Dynamic Widgets
• Bear Widgets
• Capitol One Shopping

I'm not saying there is anything particularly wrong with these apps, just trying to isolate a conflict.

Until you find a fix for the problem a workaround is to not put the computer to sleep but just have the screensaver on which will turn black once it's run its time. Since there are no rotational drives in the portable Macs not shutting down isn't that critical.

Good morning.

I'm having the same problem, I have a macbook pro 16 with m2 pro chip, running Sonoma Version 14.3 (23D56), and every time I put my Mac to sleep, I close the display lid, when I come back to the Mac after a time, it starts as if it were turned off.

I have already started in safe mode, and the problem continues.

Could anyone help or know what it could be?

How you've tested that seems to point to BetterDisplay as the culprit. You should start looking for an alternative to that app.