[CI] Use OpenAssetIO ConanCenter package

[feltech]

Closing this since

• The Conan package is now waaay out of date and needs significant changes (e.g. cpython removed as a dependency), which aren't gonna happen any time soon(?).
• We'll likely want to switch to Conan v2 even if we do still want to use Conan (e.g. Conan profiles are handled differently).
• The structure of tests is likely to change significantly in https://github.com/OpenAssetIO/OpenAssetIO-TraitGen/issues/32
• We'll probably satisfy dependencies a different way anyway, i.e. https://github.com/OpenAssetIO/OpenAssetIO/issues/1094