Adding/Assigning the list of Permission Sets to a User via APEX

 User userRecord = [ SELECT Id,Name FROM User limit 1];
List<String> permissionSetNames =new permissionSetNames();
permissionSetNames.add('PermissionSet1');//replace with your'e permission set name
permissionSetNames.add('PermissionSet2');//same here
List<PermissionSetAssignment> permissionSetAssignments = new List<PermissionSetAssignment>();
List<PermissionSet> allPermissionSets = [SELECT Id, Name FROM PermissionSet WHERE Name IN :permissionSetNames];
System.assertEquals(permissionSetNames.size(), permissionSets.size());

for (PermissionSet eachPermissionSet :allPermissionSets) {
    permissionSetAssignments.add(
        new PermissionSetAssignment(
            AssigneeId              = userRecord.Id,
            PermissionSetId         = eachPermissionSet.Id
        )
    );
}
insert permissionSetAssignments;

Hope this helps!!

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