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I'm confused. Isn't that a sequential line item level number within the sales order, not a unique order level number?

There are two things line ID and sequence number.
Line ID is unique.

The Line Sequence Number holds the internal sequence number stored for each transaction line according to the line item’s position in the sublist and is the value expected by the nlobjSublist methods setLineItemValue(name, linenum, value) and getLineItemValue(group, fldnam, linenum).
The Line ID is not related to the line item’s position in the sublist. Each line item is given a Line ID when it is created, which does not change until the line is removed regardless of the performed operations (e.g. editing the line, inserting a line item above). If the line item is removed and another line item is inserted to replace it, the new line item will have a different Line ID, but the same Line Sequence Number.

<https://www.flowinglink.com/line-id-vs-line-sequence-number/>

What happens if I want to add a new item to an existing sales order? What would I specify for the line ID?

Leave that unmapped and it will append your lines to existing doc