I am trying to figure out the stationarity of time series data Here, this plot shows the number of customers served per day from 1 jan 2018 to 31 dec 2019.
I grouped the entire data by each month and calculated the average and variance per month.
This is the average

This is the variance

I also ran an augmented dickey-fuller test and got the following result
ADF Statistic: -26.031963

p-value: 0.000000

Since, the mean and variance do not vary too much, should I infer that the data is stationary?
There are certainly more tests you could try out but by definition of the test, you can conclude that your data is stationary.
On the other hand I would be concerned with your test results. Getting a p of exactly zero, and a test statistic value of way below -3 or -4  I would look at your implementation again and check if it's right.