Fix docs version selector to include beta prereleases #60753

[deepeshraghav]

Problem

The documentation version selector currently only includes RC prereleases. As a result, beta (and alpha) documentation—such as v1.13.0-beta1 —is omitted whenever dev docs (e.g. v1.14.0-dev) are present, even though the beta documentation exists online.

This issue has affected multiple releases (e.g. 1.10, 1.13) and leads users to believe that beta documentation is missing.

Solution

This PR updates the prerelease selection logic in Documenter.Writers.HTMLWriter.expand_versions to:

• consider all prerelease types (alpha, beta, rc),
• select at most one prerelease per minor version using VersionNumber ordering (alpha < beta < rc`),
• preserve coexistence with dev documentation,
• keep the existing ordering: stable → prerelease → dev.

The change is minimal and localized to julia/doc/make.jl.

Verification

The logic was verified via static inspection and scenario simulation:

• prereleases are restricted to the minor version immediately preceding the dev version,
• exactly one prerelease is selected deterministically,
• dev documentation remains visible and is not overwritten.

Resulting selector order:
v1.12 → v1.13.0-beta1 → v1.14.0-dev

AI Usage Disclosure

AI tools were used to assist with understanding the existing code, exploring edge cases, and reviewing logic.
All code changes were written, reviewed, and validated by the me .

Related issues

Fixes #60753
Related to #50872