I need to add push notification in my web site
If a user has made payment for something... we show them alert in their account page on the website that you are now successfully connected to this community
If a user has done payment by check... we clear the payments by check through a cron job... once the job runs and payment is cleared... we show a notification to user whenever they log in saying that their check payment is cleared
A user sends a request to connect to an organisation... that organisation's admin should get an alert in their system saying that so and so person is pending approval from you.
Something similar to alerts that we get in our net banking might be... that your credit card payment is pending... something like that
Like we also get notifications on Facebook... the difference will be that instead of notifications we want to show alerts or messages directly displayed in their account
So, you want notifications in your system about payments.
In its simplest form, you could do it manually with emails, and/or popups in your application, that are loaded from DB when they login. This is sort of a manual system, and the Minimum Viable Feature could be quite easy to build yourself.
If you want it more advanced, like you mentioned, similar to Facebook's notifications button and feed. Then, yes, it might be easier to use getstream.io. It also has websocket integrations so you can get those notifications pushed in real-time. You can then also push other types of notifications in there, like for example: a notification when the user has logged in from a different browser (for security reasons).
I hope this answers your question.