fix: use per-chat plan file paths (#24268)

> This PR was authored by Mux on behalf of Mike.

Chats sharing one workspace (e.g. sibling subagents) all wrote to
`/home/coder/PLAN.md`, causing plan file collisions. This change derives
a unique plan path per chat from the workspace home directory and chat
ID.

## Changes

* `write_file`, `edit_files`, and `propose_plan` reject any `plan.md`
variant (case-insensitive) at the workspace home root, with a clear
error pointing to the chat-specific path.
* Root chats receive a `<plan-file-path>` block inlined in the main
system prompt with the concrete path.
* Prompt and tool descriptions no longer hardcode `/home/coder/PLAN.md`.
* Plan path handling is POSIX-only (forward-slash), relying on the
contract that workspace agent paths are normalized before reaching
chatd.
* Updated `ProposePlanTool.stories.tsx` to use per-chat path examples.
* Full test coverage for plan path detection, legacy-path rejection in
all three tools, inline prompt rendering, and fallback behavior.

coderd/x/chatd/chattool/planpath.go

@@ -0,0 +1,90 @@
+package chattool
+
+import (
+	"context"
+	"path"
+	"strings"
+
+	"github.com/google/uuid"
+	"golang.org/x/xerrors"
+
+	"github.com/coder/coder/v2/codersdk/workspacesdk"
+)
+
+const planFileNamePrefix = "PLAN-"
+
+// LegacySharedPlanPath is the original shared plan file path used by
+// every chat in a workspace.
+const LegacySharedPlanPath = "/home/coder/PLAN.md"
+
+// ResolveWorkspaceHome returns the workspace user's home directory.
+func ResolveWorkspaceHome(
+	ctx context.Context,
+	conn workspacesdk.AgentConn,
+) (string, error) {
+	if conn == nil {
+		return "", xerrors.New("workspace connection is required")
+	}
+
+	resp, err := conn.LS(ctx, "", workspacesdk.LSRequest{
+		Path:       []string{},
+		Relativity: workspacesdk.LSRelativityHome,
+	})
+	if err != nil {
+		return "", xerrors.Errorf("resolve workspace home: %w", err)
+	}
+
+	home := strings.TrimSpace(resp.AbsolutePathString)
+	if home == "" {
+		return "", xerrors.New("workspace home path is empty")
+	}
+
+	return home, nil
+}
+
+// PlanPathForChat returns the per-chat plan file path rooted in the
+// workspace home directory.
+func PlanPathForChat(home string, chatID uuid.UUID) string {
+	return path.Join(
+		home,
+		".coder",
+		"plans",
+		planFileNamePrefix+chatID.String()+".md",
+	)
+}
+
+// chatd consumes agent-normalized POSIX paths. Workspace agents are
+// expected to convert separators to forward slashes before these
+// helpers run.
+
+// isAbsolutePath reports whether p is an absolute POSIX path.
+func isAbsolutePath(p string) bool {
+	return path.IsAbs(p)
+}
+
+// looksLikePlanFileName reports whether the base name of requestedPath
+// is "plan.md" (case-insensitive), ignoring the directory component.
+func looksLikePlanFileName(requestedPath string) bool {
+	cleaned := path.Clean(requestedPath)
+	return strings.EqualFold(path.Base(cleaned), "plan.md")
+}
+
+// LooksLikeHomePlanFile reports whether requestedPath is a plan.md
+// variant (case-insensitive) sitting directly in the workspace home
+// directory.
+// The filename is compared case-insensitively because LLM output varies.
+func LooksLikeHomePlanFile(requestedPath, home string) bool {
+	normalized := path.Clean(requestedPath)
+	normalizedHome := path.Clean(home)
+
+	return looksLikePlanFileName(normalized) &&
+		strings.EqualFold(path.Dir(normalized), normalizedHome)
+}
+
+// looksLikeLegacySharedPlanPath reports whether requestedPath
+// matches the legacy shared plan path (case-insensitive). Used as a
+// narrow fallback when the workspace home cannot be resolved.
+func looksLikeLegacySharedPlanPath(requestedPath string) bool {
+	normalized := path.Clean(requestedPath)
+	return strings.EqualFold(normalized, LegacySharedPlanPath)
+}