How can one reconcile performing prayer with the demands of a precise and lengthy surgical operation that extends for hours, especially when occupied by it beyond the prayer time?

Prayer is the greatest pillar of Islam. It is not waived for a legally responsible person as long as their mind is sound. Allah has made things easy for His servants by permitting the combining of prayers when there is an excuse, so that the legally responsible person has no excuse for abandoning prayer. Prayer must be performed at its appointed time, and one should seek help through it for their tasks. If this becomes difficult, such that patients would be harmed, then it is permissible to combine two prayers or to alternate in performing them. If a legally responsible person is unable to perform prayer in its proper manner due to fear of harming a patient, they may perform bowing and prostrating by gesturing while still fulfilling the pillars of prayer.