Apple Watch SE 40mm- receive texts without cellular?

https://support.apple.com/en-us/HT205547

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.

The OPs watch is non cellular.

Yes you can receive calls and texts without cellular but you must have your phone with you,in bluetooth range.