Adjusted markdown alert styles closer to GitHub rendering.

[isoos]

• Follow-up to Enable/fix markdown alert blocks + style rules. #8181.
• Updated variable names to reflect the styles (e.g. -error->-caution).
• Updated rendering and colors from washed-out background (copied from dartdoc) to side border (close to GitHub).
• Reference GitHub rendering: https://docs.github.com/en/get-started/writing-on-github/getting-started-with-writing-and-formatting-on-github/basic-writing-and-formatting-syntax#alerts

Previous rendering:

After this PR: