The Syriac script did not stay in Osrhoene. It carried Syriac Christianity east along the trade routes, and the alphabet went with the missions: into Central Asia, where Sogdian writers adapted it, into Persia, and as far as China, where a stele erected at Xi an records the arrival of the faith in Syriac letters beside Chinese. Manuscripts and inscriptions in the script are found across a span that few alphabets can match.
Each borrowing worked the same way. The twenty-two letters were taken over unchanged and marked letters were added for whatever the borrowing language needed and Syriac lacked. The reversed pe of Christian Palestinian Aramaic is one such addition; the marked letters of Sogdian and Persian are others; the Garshuni signs for Arabic are others again. None of them altered the alphabet.
Two scripts further east are usually described as descending from this line, which is a stronger claim than borrowing and belongs to the history of the script rather than to any one letter.
For a reader today the practical consequence is the size of a Syriac character inventory. It contains signs that no Syriac text uses, because it has to serve texts in other languages that used these letters, and editions of manuscripts that show shapes ordinary writing does not. Counting the entries in that inventory does not count the letters of the alphabet, and the two numbers answer different questions.