All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.
It is prescribed for a person to supplicate with the mentioned supplication both in prayer and outside of it, since there is nothing to indicate that it is specific to prayer only. The ḥadīth cited by the questioner with its number in Ṣaḥīḥ al-Bukhārī is actually reported in a longer wording than what the questioner mentioned. Al-Bukhārī reported from ʿĀʾishah
that the Prophet, sallallaahu 'alayhi wa sallam, used to say:
“O Allah, I seek refuge in You from laziness and old age, from sin and debt, from the trial of the grave and the punishment of the grave, and from the trial of the Fire and the punishment of the Fire…”
We also draw attention to the fact that this ḥadīth of ʿĀʾishah
does not contain the phrase ‘and from the evils of old age’. This wording is reported in the ḥadīth of Anas in Sunan al-Nasāʾī, who said that the Messenger of Allah ﷺ used to seek refuge with these words, saying:
“O Allah, I seek refuge in You from laziness, old age, cowardice and miserliness, the evils of old age, the trial of the Dajjāl, and the punishment of the grave.”
In any case, it is legislated to supplicate with this duʿāʾ both during the prayer and outside of it.
Allah knows best.