Can I consider this scenario for the phase change of $H_2O_{(s)}$ to $H_2O_{(L)}$

Question

From a particular topic : Enthalpy changes during phase transformations.
It says in my textbook that standard state of a substance at a specified temperature is it’s pure form at 1 bar pressure.
Let’s consider the phase change for $H_2O(s)$ to $H_2O$ (L). $delta H$  of fusion with a subscript I.e - . It’s value is  6 kJ/mol is value needed for such a change.
This phase change is happening at a standard state according to my textbook.

Here . I have drawn is the image of how is the phase change happening. Mostly , I have just combined all the definition and statements.
The $delta H$ of fusion is at standard state. I.e it has a pressure of 1 bar of its own and a specified temperature. It is the amount of energy needed to melt $H_2O$ (s).
The surrounding are at a temperature = 273K and pressure = 1 atm.
When ice melts at 273K. It is converted to water at 273K. Same temperature. Pressure in scenario is always 1 atm.
I wish to confirm my scenario.

Transistor · Accepted Answer

Figure 1. The phase diagram for water. The pressure and temperature axes on this phase diagram of water are not drawn to constant scale in order to illustrate several important properties. Image source: Chem.LibreTexts.org.
The situation you are describing is circled in Figure 1. You are travelling along the horizont line through the melting point of water at 1 bar.
In engineering disciplines we don't use kJ/mol but rather work with the latent heat of fusion of water which is 334 kJ/kg.
Using that figure you can work out that a 1 kW (1 kJ/s) heating source will take 334 s (6.5 minutes) to convert 1 kg of ice at 0°C to 1 kg (1 L) of water at 0°C. If you leave the heater on for another 334 s the water temperature will rise to 79.8°C which illustrates how significant the cooling effect of melting ice is.
Now, how much ice do you need to add to a 330 ml can of drink to cool it from 20°C to 4°C?

Can I consider this scenario for the phase change of $H_2O_{(s)}$ to $H_2O_{(L)}$

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