First, your use of the term "swim lane" is incorrect. The to Do, In Progress, and Done columns are not "swim lanes". Those show the status of the issues.
Swim lanes are a way to create vertical groupings of issues. There are some default options for those swim lanes, like Epic or Story. In manually created boards (most often used with Company Managed projects) swim lanes can also be based on JQL issue filtering statements.
Also, please note that for a Team Managed project an agile board will be created automatically for the project. The swim lane functionality options are different between the board automatically created for a Team Managed project and a manually created board. And managing the configuration of these two types of boards is entirely different.
The board image that you provided looks to me like a manually created board, not the board automatically created for a Team Managed project.
The ">" to the left of the issue icons indicate that is a Swim lane that has been collapsed. It appears that the board has been set up to use Stories for the swim lane groupings. The grouping that is used for the swim lane results in that item itself not being shown in the status columns. That item becomes a header for the issues that are grouped in the swim lane. The same is true when you use the Group By option on a board automatically created with a Team managed project. The issues that is the "header" for the grouping will not move through the status columns. Only the issue within the group will move through the status columns.
This is not "incorrect" functionality. This is by design.
If you can clarify the actual problem you are trying to solve, and for which board, and we can determine if that board is the one automatically created for the Team Managed project or a manually created board, we'll be able to provide better guidance.
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