There are other options if you're not devoted to using an email
gateway specifically, including all the web-based free SMS sites
like this one (search "send free SMS" or similar):
https://afreesms.com/freesms/
I've tried one of those before (that one, I think) and it worked to
one number once, but never again after that. I tried another number
one other time and it didn't even work the first time. But you can
give it a try and see, I didn't notice any spam messages sent to the
number associated with my attempt. Or maybe the telco automatically
blocked incoming messages because it did sent lots of spam?
Another option is to get a mobile broadband modem. The software or
web interface for these often includes a way to send and receive
text messages, so you just need a SIM and it works like a phone
(and the phone service is charged the same way of course). On Linux
you can use ModemManagerGUI to send text messages with AT-command
based USB modems even though the Windows software doesn't run (and
probably even if that software doesn't support the feature).