[test] harden test_srp_server (openthread#10486)

This commit updates `test_srp_server` to wait longer after the start
of the SRP client before performing the test steps. This makes the
test more robust against random jitter which may be applied by the
client when registering.

tests/unit/test_srp_server.cpp

@@ -533,7 +533,7 @@ void TestSrpServerReject(void)
     srpClient->EnableAutoStartMode(nullptr, nullptr);
     VerifyOrQuit(srpClient->IsAutoStartModeEnabled());
 
-    AdvanceTime(2000);
+    AdvanceTime(15 * 1000);
     VerifyOrQuit(srpClient->IsRunning());
 
     SuccessOrQuit(srpClient->SetHostName(kHostName));
@@ -645,7 +645,7 @@ void TestSrpServerIgnore(void)
     srpClient->EnableAutoStartMode(nullptr, nullptr);
     VerifyOrQuit(srpClient->IsAutoStartModeEnabled());
 
-    AdvanceTime(2000);
+    AdvanceTime(15 * 1000);
     VerifyOrQuit(srpClient->IsRunning());
 
     SuccessOrQuit(srpClient->SetHostName(kHostName));
@@ -759,7 +759,7 @@ void TestSrpServerClientRemove(bool aShouldRemoveKeyLease)
     srpClient->EnableAutoStartMode(nullptr, nullptr);
     VerifyOrQuit(srpClient->IsAutoStartModeEnabled());
 
-    AdvanceTime(2000);
+    AdvanceTime(15 * 1000);
     VerifyOrQuit(srpClient->IsRunning());
 
     SuccessOrQuit(srpClient->SetHostName(kHostName));