Legally - healthcare institutions must pay for language services. In some cases there are imbursement paths.

When billing for interpreter services, the assistance should be billed under T1013 sign language or oral interpretive services, per 15 minutes.
However - in practice, there’s almost no reimbursement on that part of care. Let’s dive into the details.

There are very limited sources of third party funding for interpreters according to one study (1). According to this study it seems like most funding for language services comes from general revenues. And it seems that most commercial insurers are reluctant to reimburse providers for language services.

Medicaid Reimbursements

Some states cover the cost of language services for Medicaid patients as part of the underlying cost of the direct medical service, and will reimburse the cost of a medical interpreter as a result.
Currently, there are 14 states and 1 district that offer reimbursements for this service, including Connecticut, District of Columbia, Iowa, Idaho, Kansas, Maine, Minnesota, Montana, New Hampshire, New York, Texas (only sign language), Utah, Vermont, Washington, and Wyoming.
Regardless of whether your state offers reimbursement, it's important to keep in mind that all providers must offer language services to anyone who needs it. 

In states that do reimburse for the service, providers can claim an administrative match for 50% to 75% of translation and interpretation "claimed as an administrative expense" if they are not already reimbursed as part of the direct service rates. The specific matching rate available depends on your state's policies. 

Bottom line - given that the chances that the medical interpreting cost would be the burden of the healthcare institution - there is a need to find more cost-effective solutions for language accessibility, and tech-enabled, AI-driven solutions would probably be the most scaled and available ones.

Resources:
2023 - The Use of Interpreters in Health Centers