fix: remove initial global HTTP client usage (#20128)

This PR makes the initial steps at removing usage of the global Go HTTP
client, which was seen to have impacts on test flakiness in
https://github.com/coder/internal/issues/1020. The first commit removes
uses from tests, with the exception of one test that is tightly coupled
to the default client. The second commit makes easy/low-risk removals
from application code. This should have some impact to reduce test flakiness.

agent/agent_test.go

@@ -2027,7 +2027,8 @@ func runSubAgentMain() int {
 	ctx, cancel := context.WithTimeout(context.Background(), testutil.WaitLong)
 	defer cancel()
 	req = req.WithContext(ctx)
-	resp, err := http.DefaultClient.Do(req)
+	client := &http.Client{}
+	resp, err := client.Do(req)
 	if err != nil {
 		_, _ = fmt.Fprintf(os.Stderr, "agent connection failed: %v\n", err)
 		return 11

agent/apphealth.go

@@ -63,6 +63,7 @@ func NewAppHealthReporterWithClock(
 		// run a ticker for each app health check.
 		var mu sync.RWMutex
 		failures := make(map[uuid.UUID]int, 0)
+		client := &http.Client{}
 		for _, nextApp := range apps {
 			if !shouldStartTicker(nextApp) {
 				continue
@@ -91,7 +92,7 @@ func NewAppHealthReporterWithClock(
 						if err != nil {
 							return err
 						}
-						res, err := http.DefaultClient.Do(req)
+						res, err := client.Do(req)
 						if err != nil {
 							return err
 						}