Related Why are some bakashot made on Shabbat?
Before we get to Pesukei Dezimra, there are a variety of korbanot and related sections that we say as part of morning davening. In my Artscroll siddur, many are preceded by a short paragraph such as this Yehi Ratzon
שֶׁתְּ֒רַחֵם עָלֵֽינוּ וְתִמְחָל לָֽנוּ עַל כָּל חַטֹּאתֵֽינוּ וּתְכַפֶּר לָֽנוּ אֶת כָּל עֲוֹנוֹתֵֽינוּ וְתִסְלַח לָֽנוּ עַל־כָּל פְּשָׁעֵֽינוּ וְשֶׁתִּבְנֶה בֵּית הַמִּקְדָּשׁ בִּמְהֵרָה בְיָמֵֽינוּ וְנַקְרִיב לְפָנֶֽיךָ קָרְבַּן הַתָּמִיד שֶׁיְּ֒כַפֵּר בַּעֲדֵֽנוּ כְּמוֹ שֶׁכָּתַֽבְתָּ עָלֵֽינוּ בְּתוֹרָתֶֽךָ, עַל יְדֵי משֶׁה עַבְדֶּֽךָ, מִפִּי כְבוֹדֶֽךָ כָּאָמוּר:
Some are also followed by a paragraph such as
שֶׁתְּ֒הֵא אֲמִירָה זוּ חֲשׁוּבָה וּמְקֻבֶּֽלֶת וּמְרֻצָּה לְפָנֶֽיךָ כְּאִלּוּ הִקְרַֽבְנוּ קָרְבַּן הַתָּמִיד בְּמוֹעֲדוֹ וּבִמְקוֹמוֹ וּכְהִלְכָתוֹ...
But the Sefaria site (and my Artscroll) both say יש שאין אומרים 'יהי רצון' בשבת ויום טוב
that some skip these paragraphs on Shabbat and Yom Tov.
(side note -- my Siddur Tefillah Hashalem has other Yehi Ratzons sprinkled through the area but only indicates that they are not said by one in the middle of Eizeh Hu Mekoman and I don't know if this means that only that one isn't said on Shabbat or if that is applicable to all of them)
Why would one NOT say them on Shabbat and/or Yom Tov?
I know that there is some general idea of "not making requests" on Shabbat but that seems highly variable. We say a Yehi Ratzon right before Korbanot after the initial b'rachot (shetatzileini hayom, a singular and personal request). We say one at the very end of Shmoneh Esrei. We even have a Yehi Ratzon in the musaf Shmoneh Esrei (sheta'aleinu b'simcha).
The one before the Korban Tamid asks Hashem to treat our saying the text as if we had performed the Korban, but that shouldn't be a problem because the Tamid was offered on Shabbat also. The distinction can't be about "communal" vs. "personal" because, as this site indicates, the Tamid was communal as was the mussaf. It can't be about "not asking forgiveness" because the korban for Rosh Chodesh included an aspect of kapparah, even on Shabbat.
So why would there be any tradition of skipping the Yehi Ratzons in these cases on Shabbat and Yom Tov? (no answer in Rite and Reason, or ספר טעמי המנהגים ומקורי הדינים)
