The US apparently did:
The United States could not vote yes on a text that did not condemn Hamas or reaffirm the rights of all Member States to protect their citizens from terrorist attacks and will continue to urge the Council to condemn Hamas’ actions. However, the United States did support many of the important provisions, she said, pointing out it is the first adopted text that mentions Hamas. She fully supports the resolution’s call for the immediate and unconditional release of hostages held by Hamas and other groups. The United States has also advocated for humanitarian pauses to allow for full, rapid, safe and unhindered access to civilians in Gaza.
She said her country has clearly stated its expectation that parties to the conflict will abide by their international law obligations. “We’ve been clear at the highest levels: Hamas’ actions do not lessen Israel’s responsibility to protect innocent people in Gaza,” she said. “As Israel exercises its right and indeed its responsibility to protect its people from acts of terror, it must do so in a way that is consistent with the laws of war. I want to be clear: The United States does not want to see firefights in any hospitals.”
So, as you can see, the US mentioned "responsibility to protect" with respect to both Israelis and Palestinians. If I'm to be a bit snarky here: remark that the US [just] said that's Israel's responsibility. One of the crticisms of R2P is that countries will bandy the notion, but not claim it's their responsibility in concrete cases, unless it's also politically convenient to intervene in those for other reasons.
AFAICT, the full US statement doesn't seem to reference any of the UN docs where that concept was [attempted to be] defined before, so it might also be the case that that's just a turn of the phrase that just happens to coincide with the buzzword. YMMV.
OTOH the way the US invoked that is not incompatible with the elaborations:
in the so-called “three pillars” of R2P. First, the State carries the primary responsibility for protecting populations from genocide, war crimes, crimes against humanity and ethnic cleansing; second, the international community has a responsibility to encourage and assist States in fulfilling this responsibility; and finally, the international community has a responsibility to use appropriate diplomatic, humanitarian and other means to protect populations from these crimes. If a State is manifestly failing to protect its populations, the international community must be prepared to take collective action in accordance with the Charter of the United Nations.
The US surely doesn't consider Israel to be failing, so no need for the US to mention anything other than the 1st pillar in this case (and implicitly put themselves--the US--in the role of a 2nd pillar [participant] in doing that reminding.)
There's one other interesting point. A number of Muslim countries' leaders (like Iraq, Iran, Qatar, Turkey) have denounced Israel's action in Gaza as genocide. But interestingly enough, most of these (except Qatar) don't seem to dig the R2P concept enough to co-sponsor its last inclusion in an UN agenda. The full list of those countries is below.
Albania, Argentina, Armenia, Australia, Austria, Belgium, Botswana, Brazil,
Bulgaria, Cabo Verde, Canada, Costa Rica, Côte d’Ivoire, Croatia, Cyprus,
Czechia, Denmark, Equatorial Guinea, Estonia, Fiji, Finland, France, Georgia,
Germany, Ghana, Greece, Guatemala, Hungary, Iceland, Ireland, Italy,
Kiribati, Latvia, Lesotho, Liechtenstein, Lithuania, Luxembourg, Madagascar,
Malta, Marshall Islands, Monaco, Montenegro, Morocco, Netherlands, New
Zealand, North Macedonia, Norway, Panama, Papua New Guinea, Peru,
Poland, Portugal, Qatar, Republic of Korea, Republic of Moldova, Romania,
Rwanda, San Marino, Senegal, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Ukraine, United Kingdom of Great Britain and Northern Ireland, United States
of America, Uruguay and Zambia
Addendum
Add the following countries to the list of sponsors of the draft resolution:
Andorra, Bangladesh, Chile, Colombia, Dominican Republic, El Salvador,
Gambia, Guinea-Bissau, Malawi, Mauritania, Mauritius, Mexico, Niger,
Paraguay, Timor-Leste and Tuvalu
Besides Qatar only Morocco, Mauritania, and Bangladesh seem to be countries with a Muslim majority that co-sponsored that resolution. (Apologies if I missed some others in that lengthy list.) I'm guessing that R2P as done in Libya might have left a sour taste in other Muslim countries.
FWTW, one of Qatar leader's statements about Gaza (I could find) mentions "legal responsibilities" and "dual standards" (of the "international community") but not quite the R2P phrase. Qatar's UN rep did give a speech at the UN in June (re)affirming support for R2P, but that didn't mention Gaza.
OTOH
Erdoğan said, "Turkey has a responsibility to protect Palestinians from Israeli oppression." We are doing and will continue to do more than meet the eye.'
"It is our historical duty to speak out against the crimes of those who are supporting the immoral, unethical, despicable genocide in Gaza," the Turkish president said.
How much of that is just neo-Ottoman posturing is hard to say. Interstingly enough though, Turkey has described somewhat more concretely the role it sees for itself:
Since the outbreak of the war in Gaza, Ankara has sought a greater role in the mediation efforts, hostage negotiations, and discussions of humanitarian access. Turkish Foreign Minister Hakan Fidan has floated the idea of Turkey assuming a “guarantor” status for Gaza, suggesting at a meeting of Islamic countries in Riyadh, “The Muslim world should take bold decisions until a sovereign, independent, contiguous Palestine with East Jerusalem as its capital is established.” Erdoğan reiterated the call for Turkey’s guarantor status at an emergency meeting of the Arab League and the Organization of Islamic Cooperation in Saudi Arabia in mid-November.
More than any other regional state, Turkey seems eager to assume an international mandate for the future governance of Palestinians. While Qatar has been involved in hostage negotiations and Egypt in diplomacy around humanitarian access via the Rafah crossing, neither Egypt nor Qatar has the peacekeeping and humanitarian capacity that Turkey has built through its peacekeeping roles in Somalia, Afghanistan, and the Balkans, and its newly acquired administrative experience in parts of Turkish-controlled northern Syria.
There is an inherent contradiction in the Turkish position — wanting to lead the charge against the West/Israel and seeking visibility and leadership in a postwar settlement.
