Note: I am not a linguist, please provide any corrections for terminology.
I would like to find some approximate data (if it exists) comparing several languages with the number of different syllables in all used words of the language and in the X% most used words of the language.
I have been only able to find some (non-reliable) information for the number of different syllables in all used words of the language:
Yoon Mi Oh's 2015 thesis (pages 44-45) provides estimates of the number of syllables for various languages, gathered by taking the 20,000 most frequent words in a corpus of each language and counting the different syllables that show up. Ordering them by increasing number of syllables:
Japanese: 643
Korean: 1104
Mandarin: 1274
Cantonese: 1298
Basque: 2082
Thai: 2438
Italian: 2729
Spanish: 2778
French: 2949
Turkish: 3260
Catalan: 3600
Serbian: 3831
Finnish: 3844
Hungarian: 4325
German: 5100
Vietnamese: 5156
English: 6949
For example, her count for English is 6,949 syllables—significantly less than the 15,000 you cited, because English has a lot of possible syllables, but most of them aren't actually used. ("Wug" and "strall" follow the rules of English syllable structure, but don't actually appear in any commonly-used words.)
Page 58 of the same thesis also gives the Shannon entropy of the syllable distribution in each language, which is an alternate way of measuring it; this takes into account the fact that English has a lot of syllables, but some of them are very rare (like the syllable "strengths", it only appears in a single word), while e.g. Japanese has fewer syllables, but they're more evenly distributed. By this measure, an English syllable in isolation conveys 9.51 bits of information on average, and a Mandarin syllable conveys 8.69 bits.
Terminologically, I think you are interested in the number of "distinct syllables" in a language. "Syllabic phoneme" means, approximately, "vowels", but also syllabic consonant (as exist in some languages), and with the provision that the sound has to be contrastive and not allophonic (for instance, you would not count with [ə] and [ʌ] in English since the distribution is rule-governed).
This is not information generally available for languages, and Barker's underlying paper on English shows you why. For some languages it's a simply matter of computing and "trivial" searching, but even then, non-triviality lurks. Hawaiian has 8 consonants and 5, 10 or 25 vowels, depending on how you treat long vowels and diphthongs. If we take the smallest numbers, syllables are of the type V and CV, therefore there are 5+40 theoretically possible syllables. Then you would just search a dictionary to see if they all exist (there is a gap for [wū] and only 2 examples of [wu]). Taking the largest number, you get 25+200 (possibly minus 1 or 2). The count in English is much higher because we have more phonemes, and the possibilities for combination are greater = (C(C(C)))V(V)((((C)C)C)C). But not every C can appear in every positions: plus, as noted by Barker and every every other linguist, it's non-obvious where the syllable boundaries are in English, so you have to decide if [btʃɪk] is a syllable of English, given "Dabchick" (I would say no but I'm not here to argue with his algorithm). English is rife with syllabification restrictions (syllables can't start with [ŋ] unless you syllabify intervocalic [ŋ] as in the onset).
This person claims that Vietnamese has 17,974 syllables, but this is a product of combinatoric calculations, and it is noted that about half of them don't actually exist. That's a pretty high percentage, suggesting that there are non-accidental gaps. For instance, there is no syllable in English that begins with "bn", which linguists generally consider to be the result of a rules. There are no syllables composed of sCVC where the two consonants are the same and the vowel is short, with a tiny number of counterexamples like "stet", "stat": some linguists (Clements & Keyser, among others) have that as a systematic fact of English. There are no syllables having [bl] as the onset, [ɪ] as the nucleus, and a coronal non-sibilant as the coda (t,d,n,tʃ,dʒ): nobody has previously noticed that gap and proposed a rule. We don't know if that is just a gap in attestation, or an actual rule-governed gap.
In principle if you could get a comprehensive list of all words, including inflectional forms, for a language and could decisively parse words into syllables, you could count the number of actually attested syllables in a language. Most comprehensive word lists don't include inflected forms, and they are usually based on written forms of major national languages. Polish, for example, allows long sequences of consonants, but this extra combinatoric power is concentrated in word beginnings and word ends. In the context VC*V, it's controversial where to put the syllable break (this is the general problem of syllabification algorithms and the question of what to count).
In other words, no, not generally, there aren't many such enumerations.
ok, no, there are not over six-hundred syllables in the japanese language ! ! it is at exactly forty-eight ! no more and no less. the chart even has a name for it, 五十音図 gojūonzu 'table of 50 sounds'. the table was revised for two of the sounds, that were taken out, snd thats why there are only forty-eight; anyway, the sounds(phones) can not be isolated japanese ! ! the sounds, are essentially syllables, as a consistent by its self does not exist. over six-hundred ! ! wow'. its why the language is so unique, there are so few syllables. it's also why they have homophones out the ying-yang; they only have forty-eight possible pieces to make words with
