micky wrote:

How hard is it to send a text from a PC, if you don't know, didn't ask,
the cellular carrier for the cell phone?

Texting is a service from a cellular carrier, not some worldwide radio
broadcast from your phone.

A couple days ago I bought some elastic online, and they offer to find
it in the store and bring it out to the car.

They say when the order is ready they will text me the store's phone
number.

The webpage first said order was in process and then pending pickup. 90
minutes later I went there and they brought it out, as they said they
would.

But the text never came.

What phone number did you give them? Does that phone number have
texting (SMS) service? If so, do you have a texting app on your phone?
The Phone app bundled on your phone should handle texts.

I would have expected it the text to be sent automatically when the
order status is changed to pending pickup. But that assumes a PC can
send a text** and I thought they would have to know the cellular carrier
prefix to do that. That seems like a big hole that should be plugged.

They send their text to YOUR phone number.

You sure they do not also have an option to send you e-mail status
updates?

**Well, it can using MyPhoneExplorer, but that doesn't seem widely used.
What alternative might be built into a PC program?

I have a Google account. That gives me access to Google Voice which has
a function to send and receive texts. You can configure Google Voice to
send e-mails to you when it receives texts.