Rebirth

The official description says: Rebirth for more cash, and your plot gets an epic new look every time. That confirms a cash benefit and a visual change. It does not say whether robots, parts, Luck, or leaderboard stats reset. Because the wipe list is unknown, there is no honest 'rebirth at this level' rule. Most rebirths has its own leaderboard, so repeated rebirths are an intended visible stat. The in-game menu shown in a short highlight includes a Rebirth button next to Robots and Shop.

Use the Rebirth control on your plot menu when you choose to reset. Requirements are not published.

Finish a goal you care about before you rebirth, because the reset list is unknown. If you only care about the stated cash benefit, the description presents further rebirths as more cash, not as a one-time bonus.