I can now compile Android without error. After trying numerous things (uninstalling and reinstalling the Android framework within Rad Studio, manually installing the Android SDK and NDK), it turned out to be a single line in the project DPROJ file that was causing the issue.
The line was:
<PlatformSDK Condition="'$(PlatformSDK)'=='' And '$(Platform)'=='Android64'">AndroidSDK34.0.4_64bit.sdk</PlatformSDK>
I don't know were this line came from, or why it was there, but removing it fixed the issue.
I hope that helps anyone else having this issue.