It is hard to answer without knowing the individual developers and the company you work at. I work at Amazon and if I were to approach the same problem, I would do something like the following:
1. Understand if the consumers of the API have driven the choice or it is driven from development team. If it is consumer driven choice, you have a longer path ahead.
2. Focus on operational capabilities of the team and hopefully, point out that having three foundational tech stacks make the operations difficult.
3. Understand the skill set of your engineers and are they all comfortable moving from one tech stack to another?
4. All of these migrations are difficult and maybe start by building a facade in a commonly agreed upon tech stack to move the consumers out and then start moving one API at a time?
Use the powers vested in you in a subtle way to nudge people by providing carrots - maybe a positive impact on their career path, better recognition from other teams, cross-org influence etc.
Take your developers into confidence, be ready to explain why you want to move to a single tech stack and how it will help the team improve and be better for the developers and the consumers of the service. All the rest is about execution.