Is it permissible for officials in our current era to motivate people with Paradise to participate in public projects, by analogy with the Prophet's action (peace be upon him) when he urged the purchase of Bi'r Rumah (the Well of Rumah)?

All righteous deeds lead to Paradise. There is no harm in saying that someone who participates in paving a road or building a water station will enter Paradise, intending that these deeds are a cause for their entry into Paradise, without making a definitive judgment for a specific individual. This is because such a definitive judgment is not possible except through revelation, which ceased after the death of the Messenger of Allah, peace and blessings be upon him.