Data saver is a standard AOSP feature that only applies to metered networks. When enabled apps on the phone use less mobile data. Having data saver enabled won't have any impact on unmetered networks, such as your home WiFi.
I am not aware that having it enabled has any privacy or security implications either way.
To find out more, including how apps should support it technically, please read:
To optimize for Data Saver mode, apps should:
- Remove unnecessary images
- Use lower resolution for remaining images
- Use lower bitrate video
- Trigger existing “lite” experiences
- Compress data
- Respect metered vs. unmetered network status even when Data Saver is off
Conversely, to work well with Data Saver, apps should not:
- Autoplay videos
- Prefetch content/attachments
- Download updates / code
- Ask to be whitelisted unless background data is truly part of core functionality
- Treat whitelisting as a license to use more bandwidth