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
assertThat(getRepositoryData(repoName).getSnapshotIds(), empty());
        } else {
            for (ActionFuture<CreateSnapshotResponse> snapshotFuture : snapshotFutures) {
                assertSuccessful(snapshotFuture);
            }
        }
    }
    public void testConcurrentSnapshotWorksWithOldVersionRepo() throws Exception {
        internalCluster().startMasterOnlyNode();
        final String dataNode = internalCluster().startDataOnlyNode();
        final String repoName = "test-repo";
        final Path repoPath = randomRepoPath();
        createRepository(
            repoName,
            "mock",
            Settings.builder().put(BlobStoreRepository.CACHE_REPOSITORY_DATA.getKey(), false).put("location", repoPath)
        );
        initWithSnapshotVersion(repoName, repoPath, SnapshotsService.OLD_SNAPSHOT_FORMAT);
        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);
        final ActionFuture<CreateSnapshotResponse> createFastSnapshot = startFullSnapshot(repoName, "fast-snapshot");
        assertThat(createSlowFuture.isDone(), is(false));