The short answer is that it depends.
First of all, "background refresh" for the app must be turned on in the system settings.
It also very much depends on what device you are using to sync with your Wave, Wave Mini, or Wave Plus. Android or iOS? Android 9/10/11/12? Samsung Note or Galaxy? The Bluetooth capabilities are dependent on multiple factors.
Apple does not allow scanning for Bluetooth in background, but sometimes allows a direct connection. If an app runs too long in background, it runs less frequently or is suspended by iOS. However, this seems to vary across iOS versions.
On Android, background operation is scheduled when app opens, but you must ensure all relevant background settings have been enabled. However, if a phone is restarted without app opened again, there is no background sync scheduled.
Android requires users to allow background execution in settings, but behavior/success depends to some degree on manufacturer, which all have their own power saving modes.
If you are interested in this topic, you should know about our ethernet-connected Airthings Hub! It brings all of your devices* online, and erases the need to sync via Bluetooth. Data will always be available from anywhere with down to 5 minutes sampling intervals.
*The Hub is compatible with the Wave 2nd gen, Wave Mini and Wave Plus