Exclude non-Linux remote-server checks from the merge queue runs (#64528)

Given that the rest of the checks are run for Linux only in the merge
queue, follow the pattern here too.

Release Notes:

- N/A

.github/workflows/run_tests.yml

@@ -903,7 +903,7 @@ jobs:
     needs:
     - orchestrate
     - check_style
-    if: needs.orchestrate.outputs.run_tests == 'true'
+    if: needs.orchestrate.outputs.run_tests == 'true' && github.event_name != 'merge_group'
     runs-on: namespace-profile-mac-large
     steps:
     - name: steps::checkout_repo
@@ -933,7 +933,7 @@ jobs:
     needs:
     - orchestrate
     - check_style
-    if: needs.orchestrate.outputs.run_tests == 'true'
+    if: needs.orchestrate.outputs.run_tests == 'true' && github.event_name != 'merge_group'
     runs-on: self-32vcpu-windows-2022
     steps:
     - name: steps::checkout_repo

tooling/xtask/src/tasks/workflows/run_tests.rs

@@ -100,11 +100,12 @@ pub(crate) fn run_tests() -> Workflow {
         (Platform::Mac, Arch::AARCH64),
         (Platform::Windows, Arch::X86_64),
     ] {
-        jobs.push(
-            should_run_tests
-                .and_always()
-                .then(check_remote_server(platform, arch)),
-        );
+        let condition = if platform == Platform::Linux {
+            should_run_tests.and_always()
+        } else {
+            should_run_tests.and_not_in_merge_queue()
+        };
+        jobs.push(condition.then(check_remote_server(platform, arch)));
     }
     let ext_tests = extension_tests();
     let tests_pass = tests_pass(&jobs, &[&ext_tests.name]);