I wrote this for if just having an old Android phone in airplane mode on WiFi who just wants the banner notifications sent to their dumb phones using their cell provider's SMS email gateway, but it will work if it has a SIM installed as well. Just play around w the settings to get what you want.
Anyway, take that old Android device, put it in airplane mode, enable the WiFi & stick it on a charger somewhere out of the way. Download an app called Macrodroid. This is a free automation app similar to Tasker but simpler. Have the apps you want notifications sent from enabled & ready. In Macrodroid, add a new Macro, & give it a name. Under Triggers, scroll down to Device Events & click Notifications (if it asks for notification privileges then enable it). Choose the apps you want to be notified on your dumb phone from here. After that, go back & under the Actions box, scroll to Messaging & choose Send Email & choose SMTP. Configure the SMTP server box for your relevant email service (this will be where the emails are delivered from, not the receive settings), then on that first screen before it fill in the from email address to the one you just used, the Email Address below that (this will be your cell service SMS gateway full address), under subject highlight the box & click the 3 dots above & choose Notification App Name, below under Message Text do the same but choose both Notification Title & also Notification Text. You can experiment, but with these selections you'll get an SMS that has for instance for an email received "Email / Sender / Subject" whatever they all may be for that specific Email. And that's all you'll get. It will vary based on how notifications are seen on the system. If the Android you're running has an active service that can send SMS by itself, you can use that instead of the Email way if easier. Leave Macrodroid enabled (as well as the Macro you made) & just let her run, it'll handle the rest.