The Syriac alphabet has twenty-two letters. A modern character standard encodes considerably more Syriac signs than that, and the gap is a source of confusion that is worth taking apart, because it turns up whenever anyone tries to count.
The extra signs fall into groups. Some are ligatures, two letters written as one, of which the yudh and he ligature used in East Syriac texts is an example. Some are positional variants that a hand treats as separate shapes, such as a final form recorded in its own right. Some are letters marked for Garshuni, the writing of Arabic in Syriac characters. Some belong to other languages that borrowed the script outright: a reversed pe used in Christian Palestinian Aramaic, and marked letters added by Sogdian and Persian writers for sounds Syriac does not have. Some are the vowel points and other marks of the two pointing systems.
None of these is a twenty-third letter. The alphabet did not grow; the inventory of things that must be encodable did. That distinction is exactly the kind a standard has to make, because a standard serves editions of manuscripts as well as ordinary writing, and an edition has to be able to show what the manuscript shows.
The atlas holds the twenty-two letters and records the rest as what they are, on the letters they are built from. A count of Syriac characters and a count of Syriac letters answer different questions and neither is wrong.