Archaic and Classical Latin
First of all, the letter Z has never been common in Archaic and Classical Latin, for a number of reasons, primarily because there was no such phoneme (see more on rhotacism in Latin).
The earliest example of Z we have from Latin inscriptions is dated 81 BC, although it can be found in earlier Latin abecedaria - see my other post on this, with an image. The letter was reportedly despised by some Romans because it "dentes mortui dum exprimitur imitatur."
The only known exceptions are some Greek loans (mostly proper nouns?). After all, as Gary Miller puts it, "The letters Y and Z at the end of the alphabet were borrowed directly from Greek to represent Attic /ü/ and /zd/ (or /dz/)" (Miller 2014: 38). Note that originally ζ "was normally borrowed as s" (Miller):
word-initial: sona and zona (in Plautus mss) cf. ζώνη; Saplutus, Saplutius, or Zaplutus cf. ζάπλουτοσ ; Sosumus cf. Ζώσιμοσ (the first example is from Miller 2014, the last two are from Adams 2016: 241).
word-internal: massa cf. μᾶζα.
For a comprehensive treatment we have to look it up in Biville 1990 - which I don't have at hand now.
Secondly, there is no hard evidence to support the claim that z was realized as [ts] in Archaic or Classical Latin.
- Faliscan (the closest Italic language): Bakkum 2009 writes that “The idea that z- may have represented [ts] is difficult” (p. 85).
- Etruscan: z is generally assumed to be [ts] (Wallace 2008); although Agostiniani argues, based on typological considerations, it was a palatal affricate [tʃ].
- Oscan: z represented [ts], e.g. húrz 'garden' (<*χortos)
- Umbrian: z (?)
Sihler 1995 argues that when zeta was "carried to Italy" (borrowed into Proto-Italic? borrowed into some Italic language?), its phonetic value was [ts] (p. 194).
Leumann et al.(§9a) mention the following epigraphic evidence of the digraphs:
- zb: Lezbia (cf. Lesbia);
- zd: Artavazdis,
- zm: Zmyrna (cf. Smyrna), Zmaragdus (cf. Smaragdus), Cozmus, Azmenus.
Note that there were two spelling variants, with s and with z (the latter more accurately representing the original phonetic form in Greek - NB: regressive assimilation). The most important thing is that such digraphs were extremely rare.
Finally, it is well-known that the cluster ts is not allowed by Latin phonotactics. Re: etsi - after all, as they say, una hirundo non facit ver.
With Late Latin, it's a completely different story. Peter Stotz ([Stotz 1996, vol. 3], §283) mentions the following phonetic realizations of the letter z in post-Classical (i.e. Late and Medieval) Latin:
- [dz]: zebus (CL diebus), zabulus (CL diabolus), oze (CL hodie);
- [z]: zona, zmurdus (smurdus or smordus), thezauraria (cf. CL thesaurus);
- [tʃ]: zelum (CL caelum), zesa (CL caesa);
- [ts]: zinamomum, zynamomum, or even çinamomum (CL cinnamomum).
Data from modern Indo-European languages, such as German or Italian, in this context is irrelevant because such spelling practices clearly go back to Ancient Greek.
I have tried not to overload my answer with too many technical details, so if you'd like to know more about any specific part, do let me know.