The OpenStack Octavia API includes, in its 2.6 version, the support for listing the existing configured providers. The default one is 'amphora' (previously named 'octavia'), but there are other supported like 'ovn'

Gophercloud is missing support for listing the providers: https://docs.openstack.org/api-ref/load-balancer/v2/#providers

Octavia Providers API: https://docs.openstack.org/api-ref/load-balancer/v2/#providers
Octavia Providers API code (list providers) : https://github.com/openstack/octavia/blob/master/octavia/api/v2/controllers/provider.py#L41