Avoid write to session storage when init

[PaperStrike]

Motivation and Context

In LazyHistory lib,

• Fix undefined writing to session storage,
• Adapt strict TypeScript,
• Reorder class properties for readability,
• Use private field instead of ES # for readability and smaller bundle size.

How Has This Been Tested?

Screenshots (if appropriate):

Types of changes

• Bug fix (non-breaking change that fixes an issue)
• New feature (non-breaking change that adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Refactor (no bug fix and new feature but improvements)

Checklist:

• My change requires new tests.
• I have added tests to cover my changes.
• My change requires a change to the documentation.
• I have updated the documentation accordingly.