Hello noelle230,
What you've found so far is correct, you will need to set up Text Message Forwarding on your iPhone in order to achieve the results you're looking for! This process is outlined here: Forward SMS/MMS text messages from your iPhone to your Mac or iPad
Automatically forward texts to your other devices
1.Make sure that you're signed in to iMessage with the same Apple ID on each device:
- iPhone or iPad: Check the Apple ID shown in Settings > Messages > Send & Receive.
- Mac: Open the Messages app, choose Messages > Settings (or Preferences), then click iMessage. Check the Apple ID shown.
2.On your iPhone, go to Settings > Messages > Text Message Forwarding.
-If you don't see Text Message Forwarding, go to Settings > Messages. Turn off iMessage, then turn it back on. Tap Send & Receive, tap Use Your Apple ID for iMessage, then sign in with the same Apple ID used on your other devices.
3.Choose which devices can send and receive text messages from your iPhone:
4.If you choose a device that isn't using two-factor authentication for your Apple ID, a verification code appears on each of your other devices: enter that code on your iPhone.
As long as your iPhone is turned on and connected to Wi-Fi or a cellular network, new SMS/MMS texts can be sent and received on the devices that you added.
Specifically, step 2 may be helpful for what you're experiencing!
Take care.