I don't think any app besides iMessage can even get permission to read SMS on iOS, there are no alternative message apps I'm aware of like with android.
It used to have SMS support but they yanked it maybe a year or so ago. The big issue on the user end was, if someone deleted Signal and you used Signal for your SMS, it would keep sending them signal messages and not SMS. So you were left not realizing you were texting essentially a dead number.
...much like iMessage.
It didn't show the icon for the message status, same as any other signal message?
The regular SMS/MMS feature was removed and for good reason. Many people cried about it but it was the right call. Messages would not be E2EE and people could easily think all messages sent through Signal are safe when they weren't.
Only Signal users. The Android app used to work with SMS/MMS until a couple years ago.