One becomes a yateem (Arabic: يتيم), as referenced in the Qur'an verse you quoted, when:
- One becomes a paternal orphan, and
- One has not reached adulthood.
The Prophet ﷺ defined the upper limit of orphanhood by becoming an adult (i.e., reaching puberty according to the majority of scholars):
قَالَ عَلِيُّ بْنُ أَبِي طَالِبٍ حَفِظْتُ عَنْ رَسُولِ اللَّهِ ﷺ: لاَ يُتْمَ بَعْدَ احْتِلاَمٍ وَلاَ صُمَاتَ يَوْمٍ إِلَى اللَّيْلِ
Narrated through 'Ali ibn Abu-Talib: I memorized (a tradition) from the Messenger of Allah ﷺ: There is no orphanhood after puberty, and there is no silence for the whole day till the night.
— Sunan Abi Dawud » Book of Wills » Hadith 2873
This definition applies to any form of orphanhood, paternal or otherwise. There is a distinction in the Arabic language, though:
- The word yateem (Arabic: يتيم) means a paternal orphan.
- The word 'ajji (Arabic: عجي) means a maternal orphan.
- The word lateem (Arabic: لطيم) means both paternal and maternal orphan.
It is worth noting that the criterion of becoming an adult is not a matter that all scholars agree on.
The majority of scholars consider the criterion of adulthood being mukallaf (required to perform Islamic rituals), which starts at the onset of puberty. Their rationale is that this is the point in life that Allah considers a person able to make decisions that leads to one's final desitnation: Jannah or Jahannam; accordingly, one is of the mental capability to make decisions.
A number of scholars added an aditional criterion, which is being legally competent to manage one's wealth and property. Their rationale is that several verses (Qur'an and hadith) restrict access to one's personal wealth if one is deemed incompetent, regardless of age (see Islam Q&A 205284). Legal competence is fulfilled through either having pubic hair, or reaching the age of 15 lunar years (see Sahih Muslim » The Book on Government » Hadith 1868 a and Jami' at-Tirmidhi » Judgements From The Messenger of Allah » Hadith 1361).
From the perspective of the verses in the Qur'an or hadith that refer to orphans, they are related to paternal orphans since in Islam, it is the responsibility of the father to sustain his family:
عَنِ ابْنِ عُمَرَ ـ رضى الله عنهما ـ قَالَ سَمِعْتُ رَسُولَ اللَّهِ ﷺ يَقُولُ: كُلُّكُمْ رَاعٍ وَمَسْئُولٌ عَنْ رَعِيَّتِهِ، وَالإِمَامُ رَاعٍ وَمَسْئُولٌ عَنْ رَعِيَّتِهِ، وَالرَّجُلُ رَاعٍ فِي أَهْلِهِ وَمَسْئُولٌ عَنْ رَعِيَّتِهِ، وَالْمَرْأَةُ فِي بَيْتِ زَوْجِهَا رَاعِيَةٌ وَمَسْئُولَةٌ عَنْ رَعِيَّتِهَا، وَالْخَادِمُ فِي مَالِ سَيِّدِهِ رَاعٍ وَمَسْئُولٌ عَنْ رَعِيَّتِهِ
Narrated Ibn 'Umar: I heard Allah's Messenger ﷺ saying, "All of you are guardians and responsible for your charges: the Ruler (i.e. Imam) is a guardian and responsible for his subjects; and a man is a guardian of his family and is responsible for his charges; and a lady is a guardian in the house of her husband and is responsible for her charge; and a servant is a guardian of the property of his master and is responsible for his charge."
— Sahih Al-Bukhari » Book of Wills and Testaments » Hadith 2751
The sustenance responsibility of a parental orphan moves to the parental uncles, and not to the mother.