How can I tell if my Windows 10 laptop (Hewlett Packard Stream 11 running Windows 10 Home in S Mode) has an encrypted drive or not?
It would be clear if Device Encryption was enabled. If the option to enable Device Encryption does not exist it means you cannot enable it.
Since you are using Windows 10 Home in S Mode that is indeed the case. It also means that since BitLocker requires Windows 10 Professional you cannot enable use that.
Select the Start button, then select Settings > Update & Security > Device encryption. If Device encryption doesn't appear, it isn't available. You may be able to use standard BitLocker encryption instead. Open Device encryption setting.
Source: Windows 10 - Turn Device Encryption On
why does Microsoft have redundant offerings with Bitlocker and Device Encryption, neither of which work on my newly purchased laptop
Microsoft forces OEMs to ship compatible tablet devices with Device Encryption turned on. Device Encryption provides users an opportunity to use FDE on compatible devices.
Is there anything else I should be looking at?
You should upgrade to Windows 10 Professional in order to use BitLocker. Your inability to enable Device Encryption is likely due to your device does not satisfying the hardware requirements.
Source: Device Encryption Requirements
It is very unlikely, your inability to use Device Encryption, has anything to do with S Mode. However, I wasn’t able to find exclusive evidence, that S Mode actually supports it.
It’s possible S Mode is the source of your issues. The “unallowed dma capable bus devices detected” error is caused by your system configuration.
I've done a mountain of googling on this and I still can't tell if someone is going to be able to just steal the laptop and obtain credentials as plaintext out of a browser cache.
The lack of full disk encryption does not work like that.
