shabbat songs - Ban on Shabas fasts derived from lechem hapanim?

The Shabas table song "Ki eshm'ra Shabas" includes the following stanza:

רָשׁוּם/רָשַׁם בְּדַת הָאֵ׳ חוֹק אֶל סְגָנָיו בּוֹ לַעֲרוֹךְ לֶחֶם פָּנִים בְּפָנָיו עַל כֵּן לְהִתְעַנּוֹת בּוֹ עַל פִּי נְבוֹנָיו אָסוּר לְבַד מִיּוֹם כִּפּוּר עֲוֺנִי

It is written/He wrote in the law of God a rule for his lieutenants: to set showbread before Him on [Shabas]. Therefore, to fast on [Shabas] is by the decree of His wise ones forbidden: but for Yom Kipur.

In other words, there's a rabbinically-instituted ban on fasting on fast days if their dates happen to fall on Shabas; on Yom Kipur, however, which is Biblically rather rabbinically declared, there's no such ban, and one may [in fact must] fast.

Rabbi Yaakov Emden's sidur explains:

כתוב בתורת ה׳ (ויקרא כד ח) מצוה לכהניו לסדר בשבת לחם הפנים לפניו על השלחן בביהמ״ק ולסלק הלחם המונח משבת העבר ולאכלו בשבת ולכן אסור מד״ס לצום בשבת וכשחל בו יו״כ חובה לצום

Written in God's Torah (Lev. 24:8) is a command to His kohanim to set the showbread on the table before Him on Shabas, and to remove the bread sitting there from the previous week and eat it on Shabas. Therefore, it's forbidden by rabbinical decree to fast on Shabas. But when Yom Kipur falls on [Shabas], there's an obligation to fast.

(Translations are my own, and somewhat loose.)

Two questions:

1. Why extend the obligation to eat the showbread to a general ban on fasting? What does one have to do with the other?


2. Is there any source other than this song for saying that the ban on fasting on Shabas is derived from the laws of the showbread? [I've always understood that the ban on fasting on Shabas derives from the rules of oneg Shabas.]