If you look at my Syriac Diagram chart, which you refused to read, you'll see to the left under 'Eh that there's a vowel marking list for both Eastern and Western Syriac writing.
The vowels markings are not actual vowels. They exist to assist new learners of Syriac and help veteran Syriac readers distinguish words easily
The Eastern writing system uses a system of Dots which is influenced by Arabic's dot system which was invented specifically to quickly Arabize people by teaching them Arabic, so us Syriac-speakers fought back by making our own dot system
The Western writing system uses miniature Greek letters as the vowels. Capital Alpha for Pthakha, Lowercase Alpha for Zqapha, Epsilon for RvaSa, Eta for KhwaSa, Omega is supposed to be for "oh" sound until lowercase alpha became to sound like "oh" instead of "ah", and a combination of Upsilon and Omicron for "u" aka "oo" sound.
Both systems work out very nicely though.
Westerners can easily use the Western script because Greek letters that they're already familiar with from the Latin alphabet while most people who use Arabic can easily use the Eastern script from its dot system and Arabic employs.