baremetrics: Fix doc.md to match current bot documentation standards.

[hanyucrocks]

Fixes: #910

The doc.md for the Baremetrics bot had several issues compared to
the style used by other bots (xkcd, GIPHY):

• Remove the ## Developer Notes section, which is internal contributor
  guidance, not user-facing documentation.
• Fix a duplicate-word typo (short short descriptions).
• Reformat the Usage entry to use the inline example style.
• Add the standard "Run this bot" link after the Setup steps.

Screenshot of the revised version:

Self-review checklist

• Self-reviewed the changes for clarity and maintainability
  (variable names, code reuse, readability, etc.).

Communicate decisions, questions, and potential concerns.

• Explains differences from previous plans (e.g., issue description).
• Highlights technical choices and bugs encountered.
• Calls out remaining decisions and concerns.
• Automated tests verify logic where appropriate.

Individual commits are ready for review (see commit discipline).

• Each commit is a coherent idea.
• Commit message(s) explain reasoning and motivation for changes.

Completed manual review and testing of the following:

• Visual appearance of the changes.
• Responsiveness and internationalization.
• Strings and tooltips.
• End-to-end functionality of buttons, interactions and flows.
• Corner cases, error conditions, and easily imagined bugs.

[hanyucrocks]

I believe the CI failing is a flaky issue. Tagging @timabbott for your insights.