What is the ruling on working on a permissible project that was started with an interest-based loan? And is the earning derived from it lawful (halal), unlawful (haram), or doubtful (mushtabih)?

It is permissible to work on a permissible project if your job does not directly involve unlawful acts and does not assist in them. The company bears the burden of its own sins, as Sheikh Ibn 'Uthaymeen mentioned concerning an employee who does not write down usury, nor witness it, nor take it, nor give it.