Presumably, the Targum Yonasan is cluing us in on a miracle that occurred at the Mishkan, that the water stayed clear despite it being the same water without having been changed.

The Pardes Yosef asks, why wasn’t this miracle mentioned in the Mishna in Avos (5:5) which enumerates the various miracles that occurred in the Mikdash? The Mishna reads:

“Ten miracles were wrought for our ancestors in the Temple: [1] no woman miscarried from the odor of the sacred flesh; [2] the sacred flesh never became putrid; [3] no fly was ever seen in the slaughterhouse; [4] no emission occurred to the high priest on the Day of Atonement; [5] the rains did not extinguish the fire of the woodpile; [6] the wind did not prevail against the column of smoke; [7] no defect was found in the omer, or in the two loaves, or in the showbread; [8] the people stood pressed together, yet bowed down and had room enough; [9] never did a serpent or a scorpion harm anyone in Jerusalem; [10] and no man said to his fellow: the place is too congested for me to lodge overnight in Jerusalem.”

The Pardes Yosef quotes an answer from the HaIyun V'HaDrash, that that the neis of the Kiyor was similar to the case of the tree of Shlomo (see Yoma 21b), in that the miracle was inherent in the object that was permanently fixed in the Beis HaMikdash, whereas the Mishna in Avos is only enumerating the miracles that were performed externally on a recurrent basis.

I had a question on this answer. The Ohr HaTorah (Rav Shalom Teumim, Parshas Ki Sisa) has a long shtikl about the Kiyor. The Kiyor, like all of the other vessels, were formed by Betzalel. However, he proves (from the usage of the word "v'asisa") that Moshe Rabbeinu is also alluded to in the passuk, something we don't find by any of the other vessels. Rav Teumim goes on to say that the there were in fact two aspects to the making of the Kiyor. 1. There was the physical formation of the Kiyor, done by Betzalel 2. After it was formed and placed between the Ohel Moed and the Mizbe'ach, Moshe poured in water which then immediately* created a miraculous source of running spring water beneath the Kiyor with which the Kiyor was supplied with water throughout their time in the desert.

In the beginning of his shtikl, all of his sources leading to this conclusion are based on pesukim in Parshas Ki Sisa. He goes on to say that this idea is perhaps alluded to in the aforementioned Targum Yonasan in Parshas Pekudei.

He then asks, that the Gemara in Zevachim 22b says that until the time of Bar Katin there was a problem of the water becoming passul with lina overnight, which would seem to contradict the fact that there was this running spring. He answers that perhaps the water only was from the spring water during the daytime, from Alos to Shkia, but after that time the water turned to regular water. (He says that it would be meduyak the lashon of the Targum "kol yomaya.")

The last part is where I'd like to focus; this would suggest that the miracle was not permanent like the tree of Shlomo, rather it renewed on a recurring basis, if so it should have been mentioned in the Mishna, according to the logic of the HaIyun V'HaDerash?

Throughout my research, I'd like to suggest two other possible answers:

1. The Tosfos Yom Tov says that the Mishna is only counting those miracles which have no inference at all in the Torah. In this instance, the passuk in Pekudei does hint to this miracle.

The Sefer Midreshei Agada B'Targumim (R' Chaim Chamiel, printed 2002) says that the source of the Yonasan ben Uziel is inferred from the word "water", because we find a machlokes in the Gemara Zevachim 22b and Sotah 15b how to translate this word. The Yonasan ben Uziel is translating the word like R' Yishmael there. Since there is a Scriptual hint to this miracle, it was left out of the Mishna's list.

(See however, the HaIyun V'HaDerash who asks on this assertion of the Targum Yonasan being rooted in R' Yishamel, that it wouldn't make sense that the Targum Yonasan would be explaining the passuk not according to the Halacha, since we paskin like the Chachamim! He blibes tzarich iyun on this question. I saw an answer to this question, I forgot where, that it could be that the Targum Yonasan isn't paskining like R' Yishmael, rather he holds like the Chachamim in principle, but in reality the Kiyor had running water, and that is what Targum Yonasan is explaining.)

2. I thought to say an answer based on the Tiferes Yisrael to the Mishna in Avos, who says that the Mishna only counts the miracles that provided tangible benefit for the people in the Beis HaMikdash, as opposed to other miracles, such as the many miracles mentioned in Yoma 21b, which were just expressions of the fact that the Shechina rested in the Beis HaMikdash.

The miracle of the running water beneath Kiyor, I wanted to argue, didn't provide a tangible benefit, but was just a manifestation of Hashem's presence, and therefore isn't listed in the Mishna. However, I think this isn't true for a few reasons:

A. The fact that there was this running water made the lives of the Kohanim easier allowing them to not have to keep refilling the Kiyor with new water every day, since if it was regular water brought from an external source, it would become passul night because of lina. The Mishna includes other miracles in which the tangible "benefit" was related to the Halachic aspects, such as that there was never a pesul found in the Omer, Shtei HaLechem, and the Lechem HaPAnim.

B. And one can argue that the miracle was a tangible "convenience" benefit to the Kohanim in that they didn't have to shlep water every day (no less than the benefit mentioned in the Mishna of that the smoke went directly up, which was convenient for the Kohanim to work in clear air instead of smoky air, and the miracle that there were no flies in the slaughtering-area.

(I also don't understand how Tiferes Yisrael understands this to answer the case of the tree of Shlomo which was clearly a benefit to the Kohanim, as the Gemara later in Yoma 39a says, that the Kohanim benefited from the sale of thoe fruit! Tzarich Iyun.

2. The second possible answer I thought of is based on a machlokes in the scenarios of which the Mishna is discussing. Some say that these are miracles that only occured in the First Beis HaMikdash, others say it is also discussing the Second Beis HaMikdash. The Zera Yaakov (haara 71) says in the name of the Maharsham (Sukka 48b) that in the times of the Mishkan, the running water beneath the Kiyor originated from the well of Miriam, and after she died, it came from the same well but in the merit of Moshe. But after Moshe died, where did the water come from? Maharsham suggests that it was through the running water mentioned by the Targum Yonasan, seemingly a miraculous unknown source. However, Zera Yaakov asks, why do we need to come on to that Targum Yonasan, perhaps when Klal Yisrael came into Eretz Yisrael, they found a well, as there were probably many, from which to get the water from, and thus there was no need for a miracle at all? He blibes tzarich iyun on this question. According to this, perhaps the reason this miracle wasn't mentioned in the Mishna was because there was no miracle at all in the Beis HaMikdash, and, as mentioned, the Mishna is only listing miracles that existed in First Beis HaMikdash (or even Second Beis HaMikdash)

*immediately: This idea actually dovetails nicely with a cryptic comment of Mahar"i Shteif to the passuk in Pekudei (Shemos 40,30): "From here we see an allusion to the halacha found in the Gemara in Berachos, that one should make the beracha of netilas yadayim immediately to washing his hands.

The Biur on the bottom there says that this fits with the comment of the Targum Yonasan that the water that was in

the Kiyor was constantly "blessed" and running. I'd like to add that according to the Ohr HaTorah, the allusion can be focused on the on the aspect of the immediacy that the running water came immediately after Moshe poured it in. (Whereas the Biur is more focusing on the continuous refilling "beracha" of the running water)

HaIyun V'HaDrash (not brought by Pardes Yosef):