חֹמֶר בַּסְּמִיכָה מִבַּתְּנוּפָה וּבַתְּנוּפָה מִבַּסְּמִיכָה, שֶׁאֶחָד מֵנִיף לְכָל הַחֲבֵרִים וְאֵין אֶחָד סוֹמֵךְ לְכָל הַחֲבֵרִים. וְחֹמֶר בַּתְּנוּפָה, שֶׁהַתְּנוּפָה נוֹהֶגֶת בְּקָרְבְּנוֹת הַיָּחִיד וּבְקָרְבְּנוֹת הַצִּבּוּר, בַּחַיִּים וּבַשְּׁחוּטִין, בְּדָבָר שֶׁיֶּשׁ בּוֹ רוּחַ חַיִּים וּבְדָבָר שֶׁאֵין בּוֹ רוּחַ חַיִּים, מַה שֶּׁאֵין כֵּן בַּסְּמִיכָה.
There's something more strict about leaning [on an offering] than about waving [an offering], and [something more strict] about waving than about leaning.… More strict about waving: that waving is practiced with personal and communal offerings…, which is not the case with leaning.
(The Hebrew text, including vowels and punctuation, is Sefaria's. The translation is mine.)
But waving is practiced with just two animals offered as a communal offering: the two sh'lamim sheep offered on Shavuos. And leaning is also practiced with two communal offerings: the goat sent to the wilderness on Yom Kipur and the par heelem davar shel tzibur (the bull offered when the community follows a national ruling and thereby violates any of certain commands). Granted the latter must have been extremely rare, but the goat was offered every year just like the Shavuos sheep, so how can the mishna say that leaning is not practiced with communal offerings but waving is?