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
.setWaitForCompletion(true)
            .execute();
        awaitClusterState(state -> {
            final List<SnapshotsInProgress.Entry> snapshotsInProgress = state.custom(SnapshotsInProgress.TYPE, SnapshotsInProgress.EMPTY)
                .forRepo(repository);
            return snapshotsInProgress.size() == 2 && snapshotsInProgress.get(1).state().completed();
        });
        unblockAllDataNodes(repository);
        awaitClusterState(
            state -> state.custom(SnapshotsInProgress.TYPE, SnapshotsInProgress.EMPTY).forRepo(repository).get(0).state().completed()
        );
        unblockNode(repository, master);
        assertSuccessful(snapshot2);
        final SnapshotInfo sn1 = assertSuccessful(snapshot1);
        assertAcked(startDeleteSnapshot(repository, sn1.snapshot().getSnapshotId().getName()).get());
        assertThat(
            clusterAdmin().prepareSnapshotStatus().setSnapshots("snapshot-2").setRepository(repository).get().getSnapshots(),
            hasSize(1)
        );
    }
    public void testOutOfOrderFinalizationWithConcurrentClone() throws Exception {
        internalCluster().startMasterOnlyNode();
        final List<String> dataNodes = internalCluster().startDataOnlyNodes(2);
        final String index1 = "index-1";
        final String index2 = "index-2";
        createIndexWithContent(index1, dataNodes.get(0), dataNodes.get(1));
        createIndexWithContent(index2, dataNodes.get(1), dataNodes.get(0));
        final String repository = "test-repo";
        createRepository(repository, "mock");
        final String sourceSnapshot = "source-snapshot";