Suing does not always involve money. It can mean trying to get someone to stop doing something, or to do something. In this context, suing means filling a legal complaint against an entity for reviewal by a court. So, the Justice Department is basically accusing Texas of doing something wrong, so they sue them in order for this action to be decided by the courts. If the courts find in favour of the Justice Department, they ask Texas to stop doing what they are doing.
As an example, Trump sued the states that voted against him in the recent election. Had he won, he would not have gotten any money, but those votes would have invalidated.
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