Which companies offer API-based ACH pay-ins and payouts?

Almost any decent bank with a tech stack would be able to provide you with this service. Most banks are able to process NACHA files. At the end of the day, even if you work with an API, you’re still essentially constructing a NACHA file for submission.

Try Evolve bank, Cross River Bank, Signature Bank, Silicon Valley Bank, etc. All of these banks offer the APIs you are asking for.

From a company point of view, try Dwolla, SynapseFI, etc.