How do people send system messages to (human) clients these days?

When building apps/websites I often need to send messages to the business owner / admin.

The messages range from almost logging type messages such as

- "Payment failed for Order 123, please manually process the transaction"

to generic contact forms on a website:

- "FirstName LastName sent a message with the following text: something something something"

My knowledge is rather old and currently I just send email via smtp.

I'm finding email is becoming increasingly unreliable.

Sometimes the smtp server gets marked as a spam server which can take a few days to resolve.

Or the receiver implements a new mail filter, accidentally blocking all the messages.

More and more things are happening that result in emails not sending or arriving.

I've been looking at email api/services such as postmark, mailgun, sendgrid which seem a good idea, but I'm curious how other people handle messaging?

Emails still seems a very convenient messaging style (disregarding issues) and often requested (e.g client will just ask for these messages sent to admin@thing.com).

What are modern messaging practices? Is email still acceptable if you go via an email api? Should I be looking at something completely different?

Thanks guys