Today if we detect concurrent modification of a snapshot repository then we mark it with `CORRUPTED_REPO_GEN` which blocks further writes to try and prevent additional damage to its contents. You can remove the marker by calling the register-repository API again, but this API will discard no-op re-registrations without taking any action. You can work around this by unregistering the repository first (which may be impossible if it's still in use for searchable snapshots) or by re-registering it with some trivial setting change (which seems hacky).

We should not consider it a no-op re-registration if the repository is currently marked with `CORRUPTED_REPO_GEN`, because doing this re-registration will re-read the repo contents and clear the corruption marker and therefore is not a no-op.
server/src/internalClusterTest/java/org/elasticsearch/snapshots/ConcurrentSnapshotsIT.java
public class ConcurrentSnapshotsIT extends AbstractSnapshotIntegTestCase {
    @Override
    protected Collection<Class<? extends Plugin>> nodePlugins() {
        return Arrays.asList(MockTransportService.TestPlugin.class, MockRepository.Plugin.class);
    }
    @Override
    protected Settings nodeSettings(int nodeOrdinal, Settings otherSettings) {
        return Settings.builder()
            .put(super.nodeSettings(nodeOrdinal, otherSettings))
            .put(AbstractDisruptionTestCase.DEFAULT_SETTINGS)
            .build();
    }
    public void testLongRunningSnapshotAllowsConcurrentSnapshot() throws Exception {
        internalCluster().startMasterOnlyNode();
        final String dataNode = internalCluster().startDataOnlyNode();
        final String repoName = "test-repo";
        createRepository(repoName, "mock");
        createIndexWithContent("index-slow");
        final ActionFuture<CreateSnapshotResponse> createSlowFuture = startFullSnapshotBlockedOnDataNode(
            "slow-snapshot",
            repoName,
            dataNode
        );
        final String dataNode2 = internalCluster().startDataOnlyNode();
        ensureStableCluster(3);
        final String indexFast = "index-fast";
        createIndexWithContent(indexFast, dataNode2, dataNode);
        assertSuccessful(