Why won’t my watch send messages when I’m not near my phone
Why won’t my watch send text messages when I’m away from my phone
Apple Watch Series 7, watchOS 8
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If you have a GPS-only version, you do indeed need to be near your iPhone. If you bought the GPS+Cellular version and set it up properly with your carrier, then you should be able to send text messages without the iPhone nearby. See the 'Use a cellular network' section (and others) in:
About Bluetooth, Wi-Fi, and cellular on your Apple Watch - Apple Support