apple watch 3
does the apple watch need to be connected for text message and phone call notifications or just your iphone?
Apple Watch
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If you have a GPS only Apple Watch it can do some things via WiFi, but for many things it depends on the paired iPhone.
If you have a Cellular Apple Watch, you can do more things away from your Apple Watch (for a fee to your iPhone carrier), but for SMS/MMS your iPhone must be accessible via the Internet
Read the following webpage
https://support.apple.com/en-us/HT205547
And pay attention to this footnote
1. To receive SMS, MMS, or push notifications from
third-party apps on your cellular Apple Watch, your paired iPhone must
be powered on and connected to Wi-Fi or cellular, but it doesn't need to
be nearby. You also need to be signed in to iMessage on your iPhone.