Sorry, what? Chinese is emphatically NOT a syllabary. Characters have meaning, two characters that are pronounced the same can have different meanings. The spoken language is syllabary-ish but wide regional dialectic variations shift different characters in different ways, which could not be the case in a true syllabary.
To give you just one little example of how you are not correct:
长久 - cháng jiǔ - long time/long lasting
尝酒 - cháng jiǔ - to taste wine
Japanese uses Kanji (Chinese characters) not for their phonetic value (they’ve got two whole syllabaries for that), but for their meaning.
There are lots of characters that represent the same syllable, and complicated rules about which to use for writing common words, which helps to disambiguate the very numerous hononyms.
The "dialectical variations" are really different languages. Mandarin speakers are taught that only pronunciations vary, but a person transcribing Cantonese to Mandarin is doing translation to a degree comparable to Italian -> French. Politically this fact is not allowed in China, but ask anyone who is bilingual in Cantonese and Mandarin. Prepare to be surprised.
Mandarin and Cantonese are both widespread enough to have dialects of their own. For example, Dalian Mandarin has different tones and some syllables that don't exist in Standard Mandarin: https://en.wikipedia.org/wiki/Dalian_dialect
> There are lots of characters that represent the same syllable,
And also (less common, but existant) characters that represent different syllables in different contexts. A prominent example would be 觉, pronounced jué in 觉得 but jiào in 睡觉
Hanzi are logographs, not a syllabary.
> and complicated rules about which to use for writing common words
Maybe if you have some need to believe in the bizarre fiction that Chinese characters only provide phonetic information. In the real world, the characters have meaning and history, which simply dictates what characters to use for which word.
This is like saying English is written with logographs, not an alphabet. Kanji are logographs and not a syllabary. Hanzi are closer to being a syllabary than they are to being logographs. The sound is the primary concept.
Obviously, the characters do convey considerably more than just phonetic information. But phonetic information is the first and most important thing they carry.
It is quite remarkable how people continue to believe what their elementary teacher told them, even after years and years' experience to the contrary.
In English, people believe that "Elements of Style" is full of good advice despite everything good they have ever read violating every rule on every page.
To give you just one little example of how you are not correct:
长久 - cháng jiǔ - long time/long lasting
尝酒 - cháng jiǔ - to taste wine
Japanese uses Kanji (Chinese characters) not for their phonetic value (they’ve got two whole syllabaries for that), but for their meaning.