You might get a clue to whats going on from the device's event log. Select the 'Events' button from the device's details page; in the 'Type' column look for commands along side the app that produced them. Triggers produced by the resulting on/off events will be shown in the 'Triggered apps' column.
Adding to the above, there are more places you can check, but I agree that "Events" (in recent platform versions) for the device is generally a good place to start. Note that "triggered" just means that the listed app has a subscription to that event, so it woke up and may have done something in response. You can also look at the "Produced by" column to see what app called the command, which if it's coming from your hub should likely be something listed for something like "command-off" in your table.
See here (the linked section in particular) for more ideas:
Also, if these are Hue Bridge bulbs brought into Hubitat via the Hue integration (or a similar community offering), keep in mind that something outside Hubitat could also be affecting it. So could anything you have exposed via Alexa or other integrations. But the above should help you get started in any case.
"Switch" is the name of the attribute/event, corresponding to the on/off state of the device, which is the value. The Hue integration is fine; I was asking only because there are two ways this could be done, that (which I would recommend) or directly paired as Zigbee devices (technically possible but requires some care, another topic).
From your screenshots, the only thing I see turning the lights of from Hubitat is your app called "Lower Level" (if you click that, it will take you there, in case you don't already know what it is). In most cases, this does not seem to be what actually turns it off (except in the two two rows in your table)--there's another time the command was sent, but the device was already off.
For the times when you don't see a commmand sent from Hubitat but the device changes on its own (e.g., at 7:08:19.141 AM), something outside Hubitat must be doing it. This is one reason I asked about the Hue Bridge--Hubitat isn't the only system that can act on your devices, in that case. This could be someone using the Hue app, a Hue remote control device, voice control with Alexa or Siri if you have those enabled, an automation set up in the Hue app, or a number of other possibilities.
Here's a common one for unexpected light changes: do you have the Alexa Hunches feature turned on? This will try do things for you that it thinks you want, but you might actually not. See here for how to disable: https://www.amazon.com/gp/help/customer/display.html?nodeId=G63YSH7WU32D9GW9. This is just one possibility; I'd consider what else you may have connected with your Bridge.
No Alexa hunches. Just checked and thats turned off.
"Lower Level" is the Hubitat basic rule name that turns on/off a bunch of accent lighting in my living and family rooms.
I did use to control these accent lights directly in the Hue app as a routine before I got my hubitat. I also controlled them when I was on Smartthings but that hub is unplugged now, wonder if the Hue bridge has some phantom trace if it (it's been deleted in the app)?
Im the only one in the house with the Hue app installed so I dont think its anyone else controlling them. It's pretty odd that they turn off instantly right after they turn on though which makes me think it's not some sort of external action doing this? The timing needed would be pretty rare to execute.
Lots of SmartThings automations use the cloud, even when local would make more sense (it's one of the reasons Hubitat exists in the first place), but when I used it, the Hue integration communicated locally. I'm not sure if anything has changed. But if you haven't, it would be good to verify that the SmartApp is gone, as unplugging your hub wouldn't be enough to stop most cloud-to-cloud automations. This should have been all on the ST side, nothing configured in the Hue Bridge itself--though the Hue app (and perhaps some third-party ones) do have some options there.
I suppose another way you can rule out Hubitat is this: shut down your Hubitat hub (Settings > Shut Down), turn on the Hue light via some other means, see if the problem persists, then see if it comes back when you bring the hub back up if not. It's possible something is going on that is sneaking under the event data (regular hub Logs may also be helpful, but only if the associated app has logs enabled), but it's unlikely from what you've shared.
Resetting the Hue Bridge would require you to re-configure all connected lights and accessories and also "re-pair" it with Hubitat, Alexa, and whatever other integrations you may have set up. You certainly can do that if you want to, but unless you have a small setup, it probably won't be easy and isn't where I'd start.
I haven't seen any reports of that outside bulb failure, but similar troubleshooting as above would apply. Have you looked at "Events" to verify the assumption that no app is sending any commands? If they are in any groups, including Groups and Scenes or Room Lighting activators, be sure to check those, too.
In any case, the conjecture would not apply to the OP's problem, as Hue Bridge bulbs would not be directly paired to the hub.