Does the departure of one waiting for prayer from the mosque to renew their ablution -not because it was invalidated- interrupt the virtue of waiting for prayer and necessitate renewing the intention, by analogy with i'tikaf, or does the virtue continue?

The waiting for prayer after prayer, whose virtue is mentioned in the noble prophetic tradition, is not interrupted by leaving the mosque for ablution or other ordinary tasks at home and outside, as long as the heart remains attached to the mosque and awaiting the prayer time. This waiting means occupying one's thoughts with prayer, whether the person is sitting in the mosque, at home, or at work, with their heart attached to it. That is indeed the ribat (spiritual steadfastness/vigil).