running ../gradle --version is showing Gradle 8.9, but gradle -v shows Gradle 8.10,

This is correct. This is a case where the installed version is different than the version that is included with the project. Unless you are bootstrapping projects from scratch, you don’t really need to use an installed version. It is recommended to always use the wrapper as this prevents version incompatibilities between what’s installed and what the project was designed to work with.

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