Yechezkel's undisputed prophetic status and important leadership role in the Judahite community are currently only known from the book itself (i.e., he's not known to be mentioned in other contemporaneous or near-contemporaneous sources), which both states that he was chosen by Hashem to lead the exiles in Babylon (24:24-27), and that on several occasions he taught and prophesied before the elders of Judah and Israel (8:1; 14:1-4 20:1-3).
As already stated by @Meir in the comments, the book is traditionally thought to have been authored by Anshei Knesset Hagedolah (Bavli Bava Batra 15b). Some time later, Yechezkel was mentioned by Ben Sira (49:8)1 as one of the great leaders of previous generations that are mentioned in ch. 44-49, a section which is sometimes referred to as "The Praise of the Previous Generations" (albeit not all famous Tanachic characters appear there, while on the other hand Shimon Hatzaddik does). In the same verse, Ben Sira also referenced Ma'aseh Merkava. Ben Sira was also a book of debatable status, but was nonetheless continuously quoted, paraphrased and referenced by many sages. A paraphrase of Ben Sira even appears in Mishna Avot 4:4 as the only known preserved teaching by Rabbi Levitas of Yavneh (see e.g. here).
From the little information we have, it seems that Yechezkel was known as an important prophet and his book was considered legitimate and at least somewhat widely disseminated. The debate of the sages was not on either of those. It's important to differentiate between the debatable status of Sefer Yechezkel and the debatable status of Shir Hashirim and Kohelet. In the latter case, the sages were disputed on the question whether touching scrolls of Shir Hashirim and Kohelet would make someone's hand impure (Mishna Yadayim 3:5). The question that lies at the root of this dispute is whether Shir Hashirim and Kohelet are even holy. Not so in the case of Sefer Yechezkel, where it was a given that even if it should not be included in the canon, it was holy and must be ganuz, i.e., placed in a genizah, like other holy texts that are taken out of use. The dispute of the sages stemmed from the question of whether it was right to distribute the book to the masses and teach it to them, because it contains some material that may not be understood by all. What Chananyah ben Chizkiyah ben Giron (or Gurion in some versions) did was develop a form of homiletic exegesis for the problematic sections of Yechzekel, which made it easier to teach to the masses. No longer would sages have difficulty in explaining problematic verses as p'shat; they could now rely on Chananyah's explanations and present these verses as drash.
1 Also in R' Dr. M. Z. Segal's edition of the Hebrew medieval Cairo Genizah manuscript, p. 336, v. 11 (in Hebrew)/v. 8 in secular numeration.
2 Consider also the existence of Yechezkel manuscripts in Qumran (which some believe were stored in the late 1st century BCE [but of course, like everything in Qumran, this is debatable]), as well as the mysterious Pseudo-Ezekiel, whose dating is also disputed. And some believe that the Septuagint's translation of Ezekiel should be dated to ca. 150 BCE (see e.g., here, p. 117 and sources cited in n. 7).