TLDR? Follow the Golden Rule of Promises:
If you have a promise, you must either return it, await it, or catch it at the end of the chain.
In the case of a returned promise, it is then the responsibility of the caller to obey the Golden Rule.
Additional: Your response handler and your error handler should be written in such a way that they can never throw errors themselves, or you should follow them with another catch for peace of mind!