I have successfully built, signed, and archived my app! However, when I try to send it to App Store Connect (I've tried using Transporter and Fastlane), I get this error:
ERROR ITMS-90161: "Invalid Provisioning Profile. The provisioning profile included in the bundle com.myapp [Payload/My App.app] is invalid. [Missing code-signing certificate]. A Distribution Provisioning profile should be used when submitting apps to the App Store. For more information, visit the iOS Developer Portal."
I am indeed using a distribution provisioning profile, and I have the codesigning certificate on the machines doing the building. I've tried deleting both from all machines, then re-downloading them from Apple Developer, but that doesn't seem to have fixed the issue.
I've discovered this was a forced Bitrise configuration change I was unaware of.
The change was quietly announced on their forum: https://discuss.bitrise.io/t/xcode-archive-export-for-ios-v4-0-0/18323#breaking-changes-and-migration-guide-1
tl;dr Bitrise changed their xcodebuild step's configuration so that ExportMethod was set to development, whereas this needed it to be set to app-store. I had previously manually set it to app-store, but during an upgrade, the upgrade process unset that back to development. Setting that back to app-store fixed my issue.