Plotly - How to add count of rows to Y axis on line chart?

You need to groupby and count the rows in pandas before sending to plotly. Also, your sample does not show it, but if you expect different dates within the same month and you only care for the year/month then you need to apply some rounding before grouping (or extract the year & month from the date with data['Date'].dt.year and data['Date'].dt.month, whichever you prefer).

Take this slightly different sample with 10/2 thrown in there

import plotly.express as px

data = {'Project':  ['Project 1', 'Project 2', ' Project 3', 'Project 4', 'Project 5', 'Project 6', 'Project 7', 'Project 8', 'Project 9', 'Project 10'],
        'Date': ['10/1/2020', '10/2/2020', '11/1/2020', '12/1/2020', '12/2/2020', '12/1/2020', '2/1/2021', '2/1/2021', '3/1/2021', '4/1/2021']}

df2 = pd.DataFrame(data, columns = ['Project','Date'])
df2['Date'] = pd.to_datetime(df2['Date'])

df_grouped = (
    df2.groupby(
        # normalize all dates to start of month
        df2['Date'].astype('datetime64[M]')
    )['Project'].count().rename('Count').to_frame()
)
df_grouped['Names'] = (
    df2.groupby(df2['Date'].astype('datetime64[M]')
    )['Project'].agg(',<br>    '.join)
)

print(df_grouped)

fig = px.line(
    df_grouped, y='Count', title='<b>Projects per month</b>',
    hover_data=['Names']
)
fig.write_html('fig1.html', auto_open=True)

Update: as requested, this new code shows the project names on hover.

Output

            Count                                          Names
Date
2020-10-01      2                    Project 1,<br>    Project 2
2020-11-01      1                                      Project 3
2020-12-01      3  Project 4,<br>    Project 5,<br>    Project 6
2021-02-01      2                    Project 7,<br>    Project 8
2021-03-01      1                                      Project 9
2021-04-01      1                                     Project 10