Rework probe concept and task pages to improve separation of concerns

[kfess]

This is a Feature Request

What would you like to be added

IMO, the current concept page for probes seems thin, while the task page contains a fair amount of conceptual content and relatively new feature gate information (Probe-level terminationGracePeriodSeconds). I'd like to try to rework both pages.

move to the concept page (suggestion):

• Caution and Note callouts currently in the task page
• Overview of probe mechanisms (exec, httpGet, ...)
• A simple yaml to explain probe structure
• (key configuration fields?)
• and replace the current long introduction with a brief sentence in the task page

Why is this needed

The concept page currently does not explain probe mechanisms or key fields at all. On the other hand,
the task page duplicates conceptual content that could belong to concept page. Readers coming from the concept page have to go to task page for almost all the details.

Comment
IMO, this is a follow up of #54960

/assign

[lmktfy]

I agree; this is an area that could use a good cleanup.

/priority backlog
/remove-kind feature
/kind cleanup
/language en
/triage accepted

[lmktfy]

Bear in mind that we also have https://kubernetes.io/docs/concepts/workloads/pods/pod-lifecycle/ to consider.

For some context about the Configuration section, see PR #51899

[kfess]

I didn't know the pod-lifecycle page also contains probe-related information that isn't covered in either the concept or the task page, so I want to include it in this rework.

My plan would be to make the concept page as the hub for probe information currently scattered across all three pages. While slimming down the task page to focus on practical steps. For the pod-lifecycle page, I'd rework the probe-related content as needed.

I'd like to work on these three pages with separate PRs to keep reviewable.

[kfess]

I think what remains to be done is:

• Rework the concept page (Rework the probe concept page to be a comprehensive hub #55261)
• Slim down the task page by removing conceptual content (Simplify the probe task page by removing conceptual content #55274)
• Move the concept page to concepts/workloads/pods/probes/ and update links across the site
• Rework the probe-related section in the pod-lifecycle page to avoid duplication with the concept page