This question and its premise makes me slightly uncomfortable. The sugya referred to appears both in Berachot 34a and in Sanhedrin 99a. The Rambam, prompted by the corpus of fantastical midrashim in perek Chelek in Sanhedrin (which includes Sanhedrin 99a) explains in his introduction to perek Chelek that many such midrashim are meant to be taken allegorically. Talking practically about whether there were no physical animals in physical Eden, given the statement that זֶה עֵדֶן שֶׁלֹּא שָׁלְטָה בּוֹ עֵין כׇּל בְּרִיָּה seems to take as its premise that the discussion is to be taken literally about gashmiyus, the physical realm.
The Eden discussed by the gemara is a mystical place of reward, and its company in the discussion includes the World to Come (Olam Habah) and the Messianic Age (Yemot HaMashiach). These are three categories of reward. The Navi Yeshaya had said:
״עַיִן לֹא רָאָתָה אֱלֹהִים זוּלָתְךָ יַעֲשֶׂה לִמְחַכֵּה לוֹ״.
“And from of old they have not heard, they have not lent an ear, no eye has seen it, God, aside from You, who will do for those who await Him” (Isaiah 64:3).
and different Amoraim explain it as that all the Neviim had spoken of great things regarding X (one level of reward) but not Y (the other level of reward). And it regarding reward in the future, not the past (that is, what God will do for those who await him). Rabbi Yochanan interprets Yeshaya's statement says that the Neviim testified about the Messianic age but not the World to Come (a position Shmuel argues about). Later in the gemara in Berachot, Rabbi Shmuel bar Nachmani (or, in Sanhedrin, Rabbi Yochanan's student and frequent disputant, Resh Lakish) says that it refers to the reward in Gan Eden. I pulled together different sections of the gemara to create this dispute, but it does seem that there is not a consensus opinion about any of this. My point is that the question about animals in Eden (assuming we take this literally) might only be according the Rabbi Shmuel bar Nachmani, and others might well argue, just as there is argument on the other statements in the gemara there.
As you mention in your question, the gemara questions and clarifies Rabbi Shmuel bar Nachmani's statement, that by Eden, he means the land of Eden and not the Garden, since Adam was in Gan Eden, and there is a pasuk that states that these are two distinct places, as a river flowed out of Eden to water the garden.
While that is the analysis done by the gemara, I am not entirely convinced that this distinction is true in the mind of Rabbi Shmuel bar Nachmani / Resh Lakish or named Chazal in general. Eden is used in Biblical parallelism by the Neviim (Yeshaya 51:3, Yechezkel 28:13) which might indicate that these can be used as identical concepts. And Chazal speak of Gan Eden, opposite Gehinnom, as the reward for the righteous, e.g. Chagiga 15a:
אמר לו ר"ע רבך לא אמר כך אלא ברא צדיקים ברא רשעים ברא גן עדן ברא גיהנם כל אחד ואחד יש לו ב' חלקים אחד בגן עדן ואחד בגיהנם זכה צדיק נטל חלקו וחלק חברו בגן עדן נתחייב רשע נטל חלקו וחלק חברו בגיהנם
The counterargument would perhaps be that Gan Eden is one level of reward while Eden is an even higher level of reward. It is strange, though, that none of the Amoraim mentioned Gan Eden vs. Gan Eden distinction in the discussion in Berachot / Sanhedrin, where it would be very appropriate to do so.
I am not alone in this disagreement with what the gemara says. We also have the following, in Zohar Chadash on Bereishit 759:
אָמַר רִבִּי יִצְחָק, וְכִי גַּן עֵדֶן הוּא נִקְרָא גִנַּת אֱגוֹז. אָמַר לֵיהּ ר' יוֹחָנָן, כֵּן, נִקְרָא גִּנַּת אֱגוֹז. כְּלוֹמַר גִּנַּת עֵדֶן, מָה הָאֱגוֹז הוּא סָתוּם מִכָּל עֲבָרָיו, וְיֵשׁ עָלָיו כַּמָּה קְלִיפּוֹת. כָּךְ עֵדֶן שֶׁל מַעְלָה, הוּא סָתוּם מִכָּל עֲבָרָיו, וְיֵשׁ עָלָיו כַּמָּה שְׁמִירוֹת, שֶׁלֹּא שָׁלְטוּ לִרְאוֹת, לֹא מַלְאָךְ, וְלֹא שָׂרָף, וְלֹא חַשְׁמַל, וְלֹא עֵין נָבִיא, וְלֹא חוֹזֶה, דִּכְתִיב (ישעיה סד) עַיִן לֹא רָאָתָה אֱלֹהִים זוּלָתֶךָ.
Note that Rabbi Yitzchak and Rabbi Yochanan are speaking of Gan Eden, and are making a diyuk regarding the Gan, garden, aspect of it. And specifically regarding this garden of Eden, which is "Eden shel Maalah", Eden of Above, Rabbi Yochanan cites the aforementioned pasuk in Yeshaya that "no eye has seen it, God, aside from You", and states, like Rabbi Shmuel bar Nachmani does in our gemara, שֶׁלֹּא שָׁלְטוּ לִרְאוֹת.
The eyes which don't see in the Zohar's account, by the way, are all angelic human eyes, and no mention is made of animals.
Also, in the Zohar's account, they are speaking of "Eden of Above". Perhaps your question is about Eden of Below, meaning the one on earth, as described in parshat Bereishit, in which case one cannot make extrapolations about human or animal presence / eyesight.