fix(paths): reconcile Zi installer and loader path resolution

[ss-o]

Summary

Reconcile the published Zi installer and loader with the approved core path-resolution contract without weakening existing installer safety checks.

Current state

public/zsh/init.zsh and public/sh/install.sh already prefer XDG data, cache, and config locations, including creation of a missing XDG data parent. Their legacy behavior is not fully aligned with direct core sourcing, and relative XDG values are not rejected consistently.

Deliverables

• Consume or exactly mirror the finalized Zi core precedence and legacy-detection rules.
• Reject relative XDG base-directory values and use the specification fallbacks.
• Avoid creating a parallel empty XDG installation when a legacy install is intentionally active.
• Preserve explicit ZI_HOME, ZI[...], branch/stream, and custom repository overrides.
• Preserve the repository-identity and destructive-operation protections delivered for install.sh: destructive git reset/clean on unvalidated ZI_HOME/ZI_BIN_DIR_NAME target #175 and fix: validate zi repository identity before destructive git operations; automate checksum generation #176.
• Keep paths with spaces as single values.
• Update installer and loader documentation embedded in generated assets where applicable.

Verification

• Extend tests/installers.sh for legacy-only, XDG-only, both-present, invalid-relative, missing-parent, explicit override, and paths-with-spaces cases.
• Run sh ./tests/installers.sh and the repository's existing syntax checks.
• Verify the checked-in checksum artifacts remain generated and clean.

Dependency

Blocked on the finalized resolver contract in the Zi core sub-issue. Implementation should not invent a second precedence model.

Next action

After the core truth table is accepted, map each installer entry point to it and add failing fixtures before changing behavior.

References

• https://github.com/z-shell/src/blob/main/public/zsh/init.zsh#L13-L31
• https://github.com/z-shell/src/blob/main/public/sh/install.sh#L105-L134

[ss-o]

Local reconciliation is complete and uncommitted in the clean code/init-loader-hardening worktree behind open PR #197. The remote PR is unchanged.

Implemented:

• loader home bootstrap mirrors core legacy/XDG/both-present selection and leaves cache/config defaults to zi.zsh;
• POSIX installer rejects relative XDG data/config paths, preserves ZI_HOME, retains legacy-only installs, and follows unique existing source identity when both roots exist;
• newly created Zi home uses mode 0700;
• generated loader snippet validates absolute XDG_CONFIG_HOME;
• docs and generated checksums are synchronized.

Validation: sh ./tests/installers.sh passes 20/20 assertions, syntax and generated checksum checks pass, and git diff --check passes.

No commit, push, PR update, deployment, or migration was performed.