test: prevent expired contexts in chatd parallel subtests (#25107)

Parallel subtests in `coderd/x/chatd` reused a parent test context with
a `testutil.WaitLong` deadline, so the context could expire before a
subtest was scheduled under load. That made the subagent lifecycle tools
return plain-text context errors instead of the expected JSON payload,
causing flaky JSON unmarshal failures.

Create fresh `chatdTestContext` values inside the affected parallel
subtests and add `chatdTestContext` to the `paralleltestctx` custom
function list so this pattern is caught by `make lint`.

Closes https://github.com/coder/internal/issues/1494

Makefile

@@ -749,7 +749,7 @@ lint/go:
 	./scripts/check_codersdk_imports.sh
 	linter_ver=$$(grep -oE 'GOLANGCI_LINT_VERSION=\S+' dogfood/coder/ubuntu-26.04/Dockerfile | cut -d '=' -f 2)
 	go run github.com/golangci/golangci-lint/cmd/golangci-lint@v$$linter_ver run
-	go tool github.com/coder/paralleltestctx/cmd/paralleltestctx -custom-funcs="testutil.Context" ./...
+	go tool github.com/coder/paralleltestctx/cmd/paralleltestctx -custom-funcs="testutil.Context,chatdTestContext" ./...
 	go run ./scripts/intxcheck ./...
 .PHONY: lint/go
 

coderd/x/chatd/subagent_internal_test.go

@@ -1510,6 +1510,7 @@ func TestResolveExploreToolSnapshot(t *testing.T) {
 		t.Run(tt.name, func(t *testing.T) {
 			t.Parallel()
 
+			ctx := chatdTestContext(t)
 			gotMCPServerIDs, err := server.resolveExploreToolSnapshot(
 				ctx,
 				tt.parent,
@@ -2076,6 +2077,7 @@ func TestSpawnAgent_BlankTypeReturnsValidOptions(t *testing.T) {
 		t.Run(tt.name, func(t *testing.T) {
 			t.Parallel()
 
+			ctx := chatdTestContext(t)
 			resp := runSpawnAgentTool(ctx, t, server, parentChat, spawnAgentArgs{
 				Type:   tt.subagentType,
 				Prompt: "delegate work",
@@ -2294,6 +2296,7 @@ func TestSubagentLifecycleToolErrorsIncludePersistedSubagentType(t *testing.T) {
 		t.Run(tt.name, func(t *testing.T) {
 			t.Parallel()
 
+			ctx := chatdTestContext(t)
 			result := requireToolResponseMap(t, runSubagentTool(
 				ctx,
 				t,