How to calculate the difference of a value for multiple dates?

You'll get a better answer if you can provide the expected output. But a simple way of checking the difference between one year from the next on the same day is using groupby and diff.

import pandas as pd
df = pd.read_clipboard()

df['gasDayStartedOn'] = pd.to_datetime(df.gasDayStartedOn)
df = df.sort_values(by='gasDayStartedOn', ascending=True)

group = df.groupby([df.gasDayStartedOn.dt.day, df.gasDayStartedOn.dt.month, 'facility'])

df['diff'] = group['gasInStorage'].diff()

df
Out[1]: 
      facility gasDayStartedOn  gasInStorage  full  injection    diff
2  UGS Haidach      2021-01-09        5.5678    43        0.0     NaN
1  UGS Haidach      2022-01-08        4.3263    38        0.0     NaN
0  UGS Haidach      2022-01-09        4.3041    37        0.0 -1.2637