What are the recommended acts of worship and supplications in the month of Ramadan to increase reward, especially those that can be recited while busy with household chores?

For righteous deeds in the month of Ramadan (definition): charity, feeding the poor, Umrah (definition), and I'tikaf (spiritual retreat in a mosque).

And to allow for the repetition of phrases while working: Tasbeeh (glorifying Allah), Tahleel (declaring Allah's oneness), Takbeer (magnifying Allah), Istighfar (seeking forgiveness), Du'a (supplication), and responding to the Mu'adhdhin (caller to prayer).

Among the narrated Ahadith: - "Every Tasbeeh, Tahmeed (praising Allah), Tahleel, Takbeer, enjoining good, and forbidding evil is a charity. And two Rak'ahs (units of prayer) of Duha (forenoon prayer) suffice for that." - "Two words light on the tongue, heavy in the scales, beloved to the Most Merciful: 'Subhan Allah wa bihamdihi, Subhan Allah Al-Azim' (Glory be to Allah and praise be to Him, Glory be to Allah the Almighty)." - "Whoever says 'Subhan Allah Al-Azim wa bihamdihi' (Glory be to Allah the Almighty and praise be to Him), a palm tree will be planted for him in Paradise." - "Whoever says 'Astaghfirullah Al-Azim alladhi la ilaha illa Huwal-Hayyul-Qayyum wa atubu ilayh' (I seek forgiveness from Allah the Almighty, Whom there is no god but He, the Living, the Sustainer, and I repent to Him), his sins will be forgiven, even if he had fled from the battlefield." - "No Muslim supplicates with a supplication but Allah grants him what he asked for, or averts from him an equivalent amount of evil, as long as he does not supplicate for a sin or breaking ties of kinship." - Upon hearing the Mu'adhdhin, we say what he says, then send blessings upon the Prophet ﷺ, and ask Allah to grant him Al-Wasilah (a high station in Paradise), and whoever asks for it for him, his intercession will be incumbent upon him. - "Whoever says after the Adhan (definition): 'Allahumma Rabba hadhihi ad-da'watit-tammah was-salatil-qa'imah, ati Muhammadan al-wasilah wal-fadilah, wab'athhu maqaman mahmudan alladhi wa'adtah' (O Allah, Lord of this perfect call and the established prayer, grant Muhammad Al-Wasilah and Al-Fadilah (distinction), and raise him to the praised station which You promised him), the intercession of the Prophet ﷺ will be made incumbent upon him on the Day of Resurrection."