Change few thing in a plotly implementation

Question

I have this code and would like the final plot to look something like this at the end. Unfortunately, I'm not getting anywhere. This is my code so far:

import pandas as pd
import plotly.express as px

# DF
dic = {(1, 1, 1): 1.0, (1, 1, 2): 0.0, (1, 1, 3): 0.0, (1, 2, 1): 0.0, (1, 2, 2): 1.0, (1, 2, 3): 0.0, (1, 3, 1): 0.0, (1, 3, 2): 0.0, (1, 3, 3): 0.0, (1, 4, 1): 0.0, (1, 4, 2): 1.0, (1, 4, 3): 0.0, (1, 5, 1): 1.0, (1, 5, 2): 0.0, (1, 5, 3): 0.0, (1, 6, 1): 0.0, (1, 6, 2): 1.0, (1, 6, 3): 0.0, (1, 7, 1): 0.0, (1, 7, 2): 1.0, (1, 7, 3): 0.0, (2, 1, 1): 1.0, (2, 1, 2): 0.0, (2, 1, 3): 0.0, (2, 2, 1): 1.0, (2, 2, 2): 0.0, (2, 2, 3): 0.0, (2, 3, 1): 1.0, (2, 3, 2): 0.0, (2, 3, 3): 0.0, (2, 4, 1): 0.0, (2, 4, 2): 0.0, (2, 4, 3): 0.0, (2, 5, 1): 1.0, (2, 5, 2): 0.0, (2, 5, 3): 0.0, (2, 6, 1): 0.0, (2, 6, 2): 0.0, (2, 6, 3): 1.0, (2, 7, 1): 0.0, (2, 7, 2): 1.0, (2, 7, 3): 0.0, (3, 1, 1): 1.0, (3, 1, 2): 0.0, (3, 1, 3): 0.0, (3, 2, 1): 0.0, (3, 2, 2): 1.0, (3, 2, 3): 0.0, (3, 3, 1): 0.0, (3, 3, 2): 0.0, (3, 3, 3): 0.0, (3, 4, 1): 1.0, (3, 4, 2): 0.0, (3, 4, 3): 0.0, (3, 5, 1): 1.0, (3, 5, 2): 0.0, (3, 5, 3): 0.0, (3, 6, 1): 1.0, (3, 6, 2): 0.0, (3, 6, 3): 0.0, (3, 7, 1): 0.0, (3, 7, 2): 1.0, (3, 7, 3): 0.0}
out = (pd.Series(dic, name='worked')
         .rename_axis(['person', 'day', 'shift'])
         .reset_index()
         .assign(shift=lambda x: x['shift'].where(x['worked'].eq(1), 0))
         .pivot_table(index='person', columns='day',
                      values='shift', aggfunc='sum')
       )
df = pd.DataFrame(out)

def Plot1(df):
    df_melted = df.reset_index().melt(id_vars=['person'], var_name='day', value_name='shift')

    fig = px.scatter(df_melted, x='day', y='person', color='shift', symbol='shift',
                     color_discrete_sequence=px.colors.qualitative.Set3,
                     symbol_sequence=['square'],
                     title=f'Schedules')

    fig.update_traces(marker=dict(size=150), selector=dict(type='scatter'))
    colorbar = dict(thickness=25,
                    tickvals=[0, 1, 2, 3],
                    ticktext=['Off', 'Morning', 'Noon', 'Evening'])
    fig.update(layout_coloraxis_showscale=True, layout_coloraxis_colorbar=colorbar)
    fig.show()

    return fig

What still needs to be changed.

1. The axis labels should be "Day" and "Person".
2. The y-axis should only show the discrete values.
3. The colorbar should be labeled correctly. It should only be labeled "Shift" once and then the numbers at the top should be removed.
4. The numbers of the x/y-axis should not be at the height of the lines, but in the middle, e.g. the first area is day 1 and then day 2 and so on.
5. The squares should fill the entire 1x1 area every day and start in the middle of the field, so to speak. Thank you very much for your help.