After build 17134 ('April 2018 Update'), some people had a range of hardware problems, which I believe included mics. A solution that someone recommended is linked to below.
I have already done this as well as all the troubleshooting MS suggested. In addition to the camera driver uninstalls, I have removed and had the system update the sound driver, BlasterX Senz3d VF0810 driver. That driver is actually MSFT supplied with a date of 7/6/2018 and a version of 10.0.17713.1000.
What's weird is that the mic works for all other applications that I use like sound recorder, skype, google meet, etc. Just NOT cortana.
Thanks for the suggestion - still no love.
It is probably a Windows issue rather than a RealSense issue, since the SR300 can function as an ordinary webcam when not being used as a RealSense depth sensing camera. And the mic in the SR300 is treated like an ordinary PC webcam mic.
I located a guide to the Hey Cortana voice feature. There are options you can enable to keep the mic active.
So the issue was a windows problem. I was able to trace it to the speech recognition settings. Apparently during one of the windows upgrades, the US English Language pack was corrupted, so the speech recognition engine did not work. I reinstalled it and rebooted. All is now fine with Cortana.
Thanks for everyone's help.