I had the same issue and also spent days fiddling around trying all the steps @T-Mux tried with no success plus attempting to boot from / install from external installation media. Always hit the same error: "MSU - 37 (FCRT migration failed.);NSPOSIXErrorDomain - 2 (failed to statfs /private/var/hardware);"
However, I can verify that what @pizzarguy suggests does work. Following the instructions for Revive the firmware on the Apple T2 Security Chip using Apple Configurator 2 solved the issue, and I am now running the beta.
https://support.apple.com/en-gb/guide/apple-configurator-2/apdebea5be51/mac
skylarmb
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Same error here on a 2018 MacBook Air.
Aug	5 21:29:06 Skylars-Air osinstallersetupd[573]: bridgeOS update prepare failed: Error Domain=BOSErrorDomain Code=204 "An error occurred during preflight." UserInfo={NSLocalizedDescription=An error occurred during preflight., UpdateBundleIdentifier=com.apple.bridgeOSCustomer, NSUnderlyingError=0x7fc702334880 {Error Domain=BridgeOSSoftwareUpdateError Code=19 "MSU - 37 (FCRT migration failed.);NSPOSIXErrorDomain - 2 (failed to statfs /private/var/hardware);" UserInfo={SystemPartitionSize=1979666432, MSUErrorCode=37, MSUErrorDescription=FCRT migration failed., NSLocalizedDescription=MSU - 37 (FCRT migration failed.);NSPOSIXErrorDomain - 2 (failed to statfs /private/var/hardware);}}}
Same error here. I've tried booting to installation media and simply running from within macOS, same error every time.