tefilla - Why does it say (negatively) in אום נצורה “She sits and waits for Shabbos to go out"?

The Hoshano for Shabbos which starts אום נצורה contains the phrase
יושבת וממתנת עד כלות שבת Which I translate as “She (Khilas Yisroel) sits and waits for Shabbos to go out.”

I don’t find this very complimentary. We instituted asking in our family, “How long is Shabbos in till?” rather than “When is Shabbos out?”

Why did the paytan choose this formulation?

Answer

I don't know that "Why did the paytan choose this formulation" can be answered. I don't think that the Paytan himself ever explained his choice of formulation( I haven't seen any evidence of such, and I'm under the impression Paytanim rarely did), and everything else is speculation.

As to a question of "Why would the Paytan choose this formulation", I found in a Yesmechu pamphlet for Sukot 5770(PDF, 2nd page, under "אמרת השבת") two reasonings:

1. The Imrei Chaim of Visnitz, in Imrei Chaim, vol. 4, p 90, s.v. "א"י והי' כי תבוא", says that one should read it as יושבת וממתנת עד כלות - הנפש על - השבת( "She sits and waits until the extinguishing of the soul over the Shabbat"), so strong is the desire of Keneset Yisra'el for the Shabbat.


2. R. Yoel of Satmar interpeted the Paytan's words as meaning that Am Yisra'el sits and waits until the time of Iqar Shabbat( the required time of the Shabbat) will pass, so they can show their devotion by adding meha-Chol el ha-Qodesh, which they always long to do.