Is this kind of public bidding for government-sponsored projects legal?

There are two questions here: First, whether public bidding is legal. Your project is a government-led urban village reconstruction project. The government leads the public bidding for land acquisition, demolition and relocation. This is legal and compliant, and also required by laws and regulations. Even if the government bids, the management unit will still levy and relocate.

Secondly, related party enterprises won the bid. Judging from the situation you listed, the winning bidder is related to the management department (relocation office). Because other unsuccessful bidders are silent, this may be suspected of false bidding (others accompanying the bid). According to the information you have, you can complain to the local commission for discipline inspection.

You are not in the industry, and you don't know what's going on.