Why there is no built-in single-tab export
SpreadsheetApp gives you getBlob() on a Spreadsheet object, but that blob is always the full workbook as a PDF. There is no getSheetBlob() or equivalent. The method Google's own UI uses is an HTTP export endpoint on docs.google.com, and you can call it yourself from Apps Script.
The key parameter is gid, which is the numeric sheet ID (not the tab name, not the index). You get it with sheet.getSheetId(). Pair that with single=true in the query string, and Google's export renderer treats only that tab as the document. Leave out single=true and you get the whole workbook even with a gid set — I've been burned by that more than once.