Rather interesting that as I checked the App Store for Apple Configurator 2, I was surprised to see that they just released a new version that's only 1 day old, from 2.14 to 2.15, and there are only two notes for it:
v.2.15 1d ago
• Allow skipping the App Store pane in Setup Assistant
• Bug fixes
I bet they encapsulated the BridgeOS update in the new version.
Edit: if you have Apple Configurator 2 installed, you can run "MCU Resource Updater" and that will also update all of its assets to reflect the latest available firmwares.
Betting that "they encapsulated Bridge OS update in the new version" is a very poor bet.
Configurator is a tool that installs software configurations and firmware, pretty much like iTunes'/Finder's role of installing iOS software updates. A large part of Configurator's user base doesn't even support Macs - they administer iPhones and iPads for corporations and schools - they're loading the organizations' standard system configurations (including device management) onto multiple devices. Heck, it's role in "refreshing" Mac firmware isn't even mentioned in the App Store description.
In all cases, if there's a new version of OS/firmware available for installation, the installer package is downloaded from Apple as needed (for iOS it's called an IPSW, I don't know what they call the bridgeOS firmware installer). Imagine, for a moment, if it was necessary to update iTunes or macOS (since Finder is baked into macOS) every time there was a new dot release of iOS.
Whatever bug fixes are incorporated in this release of Apple Configurator 2, they have to do with the functioning of Apple Configurator 2. Since the problem under discussion here was not caused by using Apple Configurator 2, why suspect that a Configurator 2 bug fix has anything to do with a macOS installer failure?
Yes, Configurator 2 is the tool needed for fixing the issue, just as iTunes/Finder is the tool for reinstalling iOS when an iPhone's OS must be erased/reinstalled. If the reports about bridgeOS being the culprit are accurate, Configurator 2 will download that new version of bridgeOS from Apple's servers if and when it's necessary to fix a Mac with this issue.