Does the scientific evidence support the belief that phones and smart speakers secretly listen to us all the time?

No — controlled studies found no evidence that popular apps covertly activate the microphone and react to keywords; the data volume would be obvious, and the legal/economic risk to providers would be existential.

The fear that smartphones and smart speakers permanently eavesdrop is widespread, but the evidence is clear:

• Data-volume argument: continuous audio streaming would generate enormous data that would immediately show up in monthly data usage. Measurements show this does not happen.
• Scientific studies: in controlled investigations, researchers could not prove that popular apps secretly activate the mic and react to keywords.
• Provider statements: Facebook, Google and others categorically deny eavesdropping; the legal consequences of discovery would be existential.
• Regulatory oversight: by the time of the FS26 source, these companies were closely watched by politicians and regulators — covertly bugging billions of people would be an economic existential risk.

Tip: The "creepy targeted ad" effect is better explained by rich behavioural/location data and social-graph inference than by secret audio — you're tracked thoroughly without anyone needing to listen.