Currently, archive issue is being rolled out as per feature request https://jira.atlassian.com/browse/JRACLOUD-5843.

According to Cloud Roadmap, this will be coming soon Q4 but there is no mention of bulk archive.

Also, as per this article, it is possible to restore multiple issues but no mention of bulk archive.

Potential workaround:

use site optimizer for work items

or there is API available to archive either individual issue or based on JQL:

https://developer.atlassian.com/cloud/jira/platform/rest/v2/api-group-issues/#api-rest-api-2-issue-archive-post

1. You can create a filter in Jira UI - it would look like https://instance.atlassian.net/issues/?filter=10196
2. Use this filter in JQL in API POST /rest/api/2/issue/archive:

  --data '{
  "jql": "filter=10196"
}'