Exporting list of all objects in buckets

The most cost-effective way to export a list of all objects in a bucket is to setup an S3 inventory configuration on the bucket, which will allow you to get a list on a schedule in a CSV file, for instance.

Refer to the S3 Inventory documentation on how to achieve this.

While I do agree with Max Clements that S3 Inventory is a great alternative to using Storage Lens for this list, you can also continue to use Storage Lens as well.

Within S3 Management Console, click on Storage Lens -> Dashboards -> Click into a dashboard you want to list out-> Accounts Tab -> Scroll down and click on the "configuring a metrics export" link.

From this link, scroll to the bottom -> Enable metrics exports -> Specify encryption/bucket location -> Save changes

From here, you would receive a metrics export into that S3 bucket once per day. You can change the bucket location or disable metrics export within the dashboard's configuration settings.