Hi
Apple Watch can pair and sync with compatible gym equipment, including sharing heart rate data to it, by following the instructions here:
Use gym equipment with Apple Watch
That is not otherwise possible via the built-in apps.
If you would like to submit a feature request to Apple, then you can do so here:
Feedback - Apple Watch - Apple
You may find that a third-party app meets your needs. Apps that may wish to consider include, for example:
FITIV Pulse Heart Rate Monitor on the App Store
- "Live stream your heart rate and other workout metrics from Apple Watch to iPhone."
To browse and search for this and/or other third-party apps with the results pre-filtered to include only those iPhone apps that also include an app for Apple Watch, use the Watch app on your iPhone. Apps can be searched by keyword or app name via the Search tab or browsed via the App Store tab. Follow the instructions here to add and use compatible apps on your Apple Watch:
Use apps on your Apple Watch - Apple Support