[Docs][CI] Enable version switcher during local and PR preview builds

[AlenkaF]

Describe the enhancement requested

Currently, the version switcher is not functional in local builds or in PR preview docs via crossbow, since it relies on the versions.json file from the arrow site.

This makes it difficult to test changes to the switcher configuration or verify that nothing breaks with new theme updates.

We should support enabling the version switcher in a dev setup, ideally by:

• Using the source versions.json file when building locally or in PR preview
• Falling back to the arrow-site JSON only in the actual deployment

This would improve confidence in docs changes and simplify local testing.

Component(s)

Continuous Integration, Documentation