The definition of the shahādatayn (the two testimonies of Islam) as explained by Al-Hāzimi comprised of three affirmations and one negation:
- Testify verbally
- Understand the meaning of the testimonies
- Act accordingly
- Refrain from saying or doing what violates or breaks either testimony.
So the definition of shahāda 'amaliyya is line 3.
In his book about the meaning of declaring there is no deity other than Allah, Sharh Kitāb at-Tawhīd 14/4 (Arabic only), Abdur-Rahman ibn Mohammad ibn Qāssim al-'Āsimi is quoted saying:
أصل التوحيد، وإن شئت قل: ماهية التوحيد، وهذه يستوي فيها كل من دخل في الإسلام أتى بشهادة أن لا اله الله وأن محمدًا رسول الله على المعنى المعهود عند أهل السنة والجماعة ولم يأت بناقض، تكلم بالشهادتين وعلم معناهما وعمل بمقتضاهما ولم يأت بناقض، هذا حكم من يُحكم عليه بأنه مسلم، هذا هو المسلم في الشريعة
NOTE. My own translation, so treat with care.
The origin of tawhīd, and if you wish, the definition of tawhīd from the Sunnis' view — and everyone who embraces Islam is equally required to do so is to bring forth the testimony that there is no deity other than Allah and that Muhammad is the Messenger of Allah without violating [the testimony] — is to say the shahādatyn, understand their meaning, (3) acts accordingly, and (4) does not violate them, then this person is deemed Muslim, and this is the definition of the Muslim in Sharī'ah.
The sect that claims that it suffices to just believe within oneself in the truthfulness of the shahādatayn without the need to say or do what affirms them is called al-Jahmiyya, not to be confused with al-Murji'a sect that claim it suffices to believe in and verbally declare the two testimonies without the need to support such beliefs by actions.
When asked about the sect of al-Jahmiyya, Al-Hasan al-Basri said, as documented by Ibn Taymiyyah - Wikipedia in Majmū' al-Fatāwa 3/103:
ليس الإيمان بالتحلي ولا بالتمني ولكن ما وقر في القلب وصدقه العمل
NOTE. My own translation, so treat with care.
Faith is not a matter of adornment or wishes; rather, it is that which resides in the heart and is confirmed by actions.
The amount of verses in the Qur'an that show the necessity of acting on one's belief is high. Here are a few examples:
وَمَنْ أَحْسَنُ قَوْلًا مِّمَّن دَعَا إِلَى اللَّهِ وَعَمِلَ صَالِحًا وَقَالَ إِنَّنِي مِنَ الْمُسْلِمِينَ
And who is better in speech than one who invites to Allah and does righteousness and says, "Indeed, I am of the Muslims."
— Surat Fussilat 41:33
إِنَّ الَّذِينَ آمَنُوا وَعَمِلُوا الصَّالِحَاتِ لَهُمْ جَنَّاتُ النَّعِيمِ
Indeed, those who believe and do righteous deeds - for them are the Gardens of Pleasure.
— Surat Luqman 31:8
إِنَّ الَّذِينَ آمَنُوا وَعَمِلُوا الصَّالِحَاتِ وَأَخْبَتُوا إِلَىٰ رَبِّهِمْ أُولَٰئِكَ أَصْحَابُ الْجَنَّةِ ۖ هُمْ فِيهَا خَالِدُونَ
Indeed, they who have believed and done righteous deeds and humbled themselves to their Lord - those are the companions of Paradise; they will abide eternally therein.
— Surat Hud 11:23
إِنَّ الَّذِينَ آمَنُوا وَعَمِلُوا الصَّالِحَاتِ يَهْدِيهِمْ رَبُّهُم بِإِيمَانِهِمْ ۖ تَجْرِي مِن تَحْتِهِمُ الْأَنْهَارُ فِي جَنَّاتِ النَّعِيمِ
Indeed, those who have believed and done righteous deeds - their Lord will guide them because of their faith. Beneath them, rivers will flow in the Gardens of Pleasure.
— Surat Yunus 10:9
إِنَّ الَّذِينَ آمَنُوا وَعَمِلُوا الصَّالِحَاتِ كَانَتْ لَهُمْ جَنَّاتُ الْفِرْدَوْسِ نُزُلًا
Indeed, those who have believed and done righteous deeds - they will have the Gardens of Paradise as a lodging,
— Surat Al-Kahf 18:107
Furthermore, the Qur'an shows us that those who kept their knowledge within themselves and either refrained from acting accordingly or acted to the opposite of their beliefs were deemed as disbelievers. The Pharaoh knew within himself that the nine signs given to Mussa ﷺ were all from Allah:
قَالَ لَقَدْ عَلِمْتَ مَا أَنزَلَ هَٰؤُلَاءِ إِلَّا رَبُّ السَّمَاوَاتِ وَالْأَرْضِ بَصَائِرَ وَإِنِّي لَأَظُنُّكَ يَا فِرْعَوْنُ مَثْبُورًا
[Moses] said, "You have already known that none has sent down these [signs] except the Lord of the heavens and the earth as evidence, and indeed I think, O Pharaoh, that you are destroyed."
— Surat Al-Isra 17:102
Anytime there was a punishment associated with any such sign, he and his people were the first to go to Mussa ﷺ asking him to supplicate to Allah to lift the punishment off (see Qur'an 7:134). They knew that Allah was the true God within themselves, but this internal belief was of no value.
In Fat'h al-Majīd 3/10, the story of the Prophet ﷺ with the disbelievers of Mecca early on within a few years of the start of the revelation shows that those disbelievers had a better understanding of the application requirements of the shahādatayn more a good portion of today's Muslims:
فلما جاءهم النبي صلى الله عليه وسلم يقول: قولوا كلمة واحدة أضمن لكم بها الجنة، قولوها كلمة واحدة أشهد لكم بها عند الله. قالوا: قل مائة كلمة نقول لك الذي تريد. قال: قولوا: لا إله إلا الله. قالوا: أما هذا فلا نريده
NOTE. My own translation, so treat with care.
So when the Prophet ﷺ came to them and said: "Say one phrase and I will guarantee paradise for you, only one phrase that I testify by for your sake in front of Allah." They said: "Ask for a hundred phrases and we will give you what you want." He said: "Say 'there is no deity other than Allah." They said: "And this is what we do not will to do."
To the disbelievers in Mecca, they grasped the meaning of the shahādatyn. They are not mere words one says out loud; rather, action has to demonstrate one's belief of what one testifies. They knew within themselves that the Prophet ﷺ was bringing them the true message from Allah, but they chose to reject it and that rendered them in a state of disbelief:
قَدْ نَعْلَمُ إِنَّهُ لَيَحْزُنُكَ الَّذِي يَقُولُونَ ۖ فَإِنَّهُمْ لَا يُكَذِّبُونَكَ وَلَٰكِنَّ الظَّالِمِينَ بِآيَاتِ اللَّهِ يَجْحَدُونَ
We know that you, [O Muhammad], are saddened by what they say. And indeed, they do not call you untruthful, but it is the verses of Allah that the wrongdoers reject.
— Surat Al-An'am 6:33
Finally, the disbelievers will request at the time of their death that they are returned to life for what: it is to do righteous deeds (acts) as is mentioned in the Qur'an:
حَتَّىٰ إِذَا جَاءَ أَحَدَهُمُ الْمَوْتُ قَالَ رَبِّ ارْجِعُونِ لَعَلِّي أَعْمَلُ صَالِحًا فِيمَا تَرَكْتُ كَلَّا إِنَّهَا كَلِمَةٌ هُوَ قَائِلُهَا وَمِن وَرَائِهِم بَرْزَخٌ إِلَىٰ يَوْمِ يُبْعَثُونَ
[For such is the state of the disbelievers], until, when death comes to one of them, he says, "My Lord, send me back that I might do righteousness in that which I left behind." No! It is only a word he is saying; and behind them is a barrier until the Day they are resurrected.
— Surat Al-Mu'minun 23:99-100