I don't know exactly for what reasons, but when I tested a Shortcut ChatGPT For Siri, I found that iPhone does not respond to Hey Siri. Vocal commands with “Hey Siri"They were ignored, as if iPhone didn't even hear about Apple's vocal assistant.
When Siri does not justify when you want to give them voice commands, the causes can be multiple. First of all you have to check if there is somehow, it is disabled from iOS settings, or if Siri is set to answer you and when iPhone is on Silent Mode.
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What do you have to do if the iPhone doesn't respond to Hey Siri?
Daca Siri nu iti raspunde pe iPhone la comanda vocala de Hey Siri, verifica in primul rand daca asistentul vocal Apple este activat pe device.
Activation Siri on iPhone for command "Hey Siri"
Mergi pe iOS in: Settings → Siri & Search → Listen for “Hey Siri” → Enable Siri.

Dupa ce apesi pe “Enable Siri“, o sa fie nevoie sa urmezi pasii prin care sa setezi Siri. Ti se vor da cateva texte pe care trebuie sa le citesti cu voce clara, pentru ca Siri sa te poata intelege.

Odata terminat de configurat Siri, pentru comanda Hey Siri, poti face primele teste.
Disabling and activating Siri on iPhone
Daca aveai deja Siri activat pe iPhone, insa nu raspundea la comanda vocala Hey Siri, poti incerca sa dezactivezi si sa activezi la loc optiunea Listen for “Hey Siri”.
Activeaza Siri cand iPhone este pe Silent Mode
Atunci cand iPhone este pe Silent Mode, Siri will not answer you to the requests from the order "Hey Siri". To activate "Hey Siri" when iPhone is on the silent mode, go on iOS in: Settings → Siri & Search → Siri Responses. Here you will need to activate the option ”Prefer Spoken Responses"To hear the Siri answers and in Silent Mode.

Once this option is activated, Siri will respond to the order "Hey Siri", even if the iPhone is on the silent mode.
In the situation where the above settings do not give results, you can Delete your interactive history with Siri, then restart iPhone. For me this method was the solution.