What does the Quran say about hope and mercy?

۞ قُلْ يَٰعِبَادِىَ ٱلَّذِينَ أَسْرَفُوا۟ عَلَىٰٓ أَنفُسِهِمْ لَا تَقْنَطُوا۟ مِن رَّحْمَةِ ٱللَّهِ ۚ إِنَّ ٱللَّهَ يَغْفِرُ ٱلذُّنُوبَ جَمِيعًا ۚ إِنَّهُۥ هُوَ ٱلْغَفُورُ ٱلرَّحِيمُ

Say, "O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful."

قَالَ وَمَن يَقْنَطُ مِن رَّحْمَةِ رَبِّهِۦٓ إِلَّا ٱلضَّآلُّونَ

He said, "And who despairs of the mercy of his Lord except for those astray?"

يَٰبَنِىَّ ٱذْهَبُوا۟ فَتَحَسَّسُوا۟ مِن يُوسُفَ وَأَخِيهِ وَلَا تَا۟يْـَٔسُوا۟ مِن رَّوْحِ ٱللَّهِ ۖ إِنَّهُۥ لَا يَا۟يْـَٔسُ مِن رَّوْحِ ٱللَّهِ إِلَّا ٱلْقَوْمُ ٱلْكَٰفِرُونَ

O my sons, go and find out about Joseph and his brother and despair not of relief from Allah. Indeed, no one despairs of relief from Allah except the disbelieving people."

وَإِذَا سَأَلَكَ عِبَادِى عَنِّى فَإِنِّى قَرِيبٌ ۖ أُجِيبُ دَعْوَةَ ٱلدَّاعِ إِذَا دَعَانِ ۖ فَلْيَسْتَجِيبُوا۟ لِى وَلْيُؤْمِنُوا۟ بِى لَعَلَّهُمْ يَرْشُدُونَ

And when My servants ask you, [O Muhammad], concerning Me - indeed I am near. I respond to the invocation of the supplicant when he calls upon Me. So let them respond to Me [by obedience] and believe in Me that they may be [rightly] guided.

وَقَالَ رَبُّكُمُ ٱدْعُونِىٓ أَسْتَجِبْ لَكُمْ ۚ إِنَّ ٱلَّذِينَ يَسْتَكْبِرُونَ عَنْ عِبَادَتِى سَيَدْخُلُونَ جَهَنَّمَ دَاخِرِينَ

And your Lord says, "Call upon Me; I will respond to you." Indeed, those who disdain My worship will enter Hell [rendered] contemptible.

فَإِنَّ مَعَ ٱلْعُسْرِ يُسْرًا

For indeed, with hardship [will be] ease.

إِنَّ مَعَ ٱلْعُسْرِ يُسْرًۭا

Indeed, with hardship [will be] ease.

وَيَرْزُقْهُ مِنْ حَيْثُ لَا يَحْتَسِبُ ۚ وَمَن يَتَوَكَّلْ عَلَى ٱللَّهِ فَهُوَ حَسْبُهُۥٓ ۚ إِنَّ ٱللَّهَ بَٰلِغُ أَمْرِهِۦ ۚ قَدْ جَعَلَ ٱللَّهُ لِكُلِّ شَىْءٍۢ قَدْرًۭا

And will provide for him from where he does not expect. And whoever relies upon Allah - then He is sufficient for him. Indeed, Allah will accomplish His purpose. Allah has already set for everything a [decreed] extent.