繰り越す: remaining work and part of an unused budget
Compare the decision to carry remaining work to the next day with the actual carryover of part of an unused budget to the following fiscal year.
Identify the object and its next period
繰り越す (くりこす) means to carry over. The work example uses 翌日, the next day, while the budget example uses 次年度, the following fiscal year, to identify the period of the carryover.
Keep each time unit with its own object. The work sentence reports a decision to carry over; the budget sentence reports an actual carryover.
A work decision and a budget result
「残った作業は翌日に繰り越すことにした。」 (We decided to carry the remaining work over to the next day.) The object is the remaining work and the destination is the next day. ことにした states a decision. It does not say that the work was canceled or completed the next day.
「使わなかった予算の一部を次年度へ繰り越した。」 (Part of the unused budget was carried over to the following fiscal year.) The actual carryover concerns 一部, part of the unused budget. Retain that scope rather than treating the entire budget, or money already used, as the amount carried over.
Preserve the partial scope and action status
残った作業 and 使わなかった予算の一部 identify the two objects. Removing 一部 from the explanation would enlarge the budget carryover beyond what the sentence says.
繰り越すことにした and 繰り越した distinguish the decision from the reported act. Read the object, the next period and that status together, without adding when the remaining work was later completed.
Was the whole budget carried over to the following fiscal year?
Show the answer and why
The sentence reports the carryover of part of the unused budget. 一部 limits the amount; it does not include the entire budget or money that had already been spent.