mcp: migrate healthcheck tool to call pkg/functions directly

[vishal-iiserb]

Part of the phased migration in #3771.
Next candidate: describe.

What changed###

• tools_healthcheck.go: handler now calls s.client.List(ctx, "") via
  pkg/functions directly to verify cluster connectivity, replacing the
  server-only liveness check.
• mcp.go: added client *fn.Client field to Server, initialized in
  New(), and added WithClient option for test injection.
• tools_healthcheck_test.go: new tests for cluster-reachable,
  cluster-unreachable, and output schema shape — no subprocess involved.

Why###

The previous healthcheck only confirmed the MCP process was alive. Agents
had no way to know if the underlying cluster was reachable before calling
other tools. This change surfaces that information as a typed field.

Tests###

go test ./pkg/mcp/... -v — all pass including 4 new healthcheck tests.

Fixes: part of #3771

[knative-prow]

[APPROVALNOTIFIER] This PR is NOT APPROVED

This pull-request has been approved by: vishal-iiserb
Once this PR has been reviewed and has the lgtm label, please assign gauron99 for approval. For more information see the Code Review Process.

The full list of commands accepted by this bot can be found here.

Details

Needs approval from an approver in each of these files:

• OWNERS

Approvers can indicate their approval by writing /approve in a comment
Approvers can cancel approval by writing /approve cancel in a comment

[linux-foundation-easycla]

• ❌ - login: @yashanand1000 / name: Yash Anand. The commit (fd435bf) is not authorized under a signed CLA. Please click here to be authorized. For further assistance with EasyCLA, please visit our EasyCLA portal and chat with our support bot.

[knative-prow]

Welcome @vishal-iiserb! It looks like this is your first PR to knative/func 🎉

[knative-prow]

Hi @vishal-iiserb. Thanks for your PR.

I'm waiting for a knative member to verify that this patch is reasonable to test. If it is, they should reply with /ok-to-test on its own line. Until that is done, I will not automatically test new commits in this PR, but the usual testing commands by org members will still work.

Regular contributors should join the org to skip this step.

Once the patch is verified, the new status will be reflected by the ok-to-test label.

I understand the commands that are listed here.

Details

Instructions for interacting with me using PR comments are available here. If you have questions or suggestions related to my behavior, please file an issue against the kubernetes-sigs/prow repository.