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.

cli/server_test.go

@@ -1254,8 +1254,9 @@ func TestServer(t *testing.T) {
 					t.Logf("error creating request: %s", err.Error())
 					return false
 				}
+				client := &http.Client{}
 				// nolint:bodyclose
-				res, err := http.DefaultClient.Do(req)
+				res, err := client.Do(req)
 				if err != nil {
 					t.Logf("error hitting prometheus endpoint: %s", err.Error())
 					return false
@@ -1316,8 +1317,9 @@ func TestServer(t *testing.T) {
 					t.Logf("error creating request: %s", err.Error())
 					return false
 				}
+				client := &http.Client{}
 				// nolint:bodyclose
-				res, err := http.DefaultClient.Do(req)
+				res, err := client.Do(req)
 				if err != nil {
 					t.Logf("error hitting prometheus endpoint: %s", err.Error())
 					return false