How does Hashicorp adopting a new BSL license affect the future of Pulumi? Will all providers start migrating away from Terraform modules, or just not receive updates?

Per their FAQs, the providers, SDKs, and Frameworks remain MPL.

...for now

Does pulumi use anything else other than terraform providers? I would expect pulumi to fall into the category of products that are a "competitor for hashicorp", as they say.

yes

We (Pulumi) made a quick statement last night on Twitter/X:

Pulumi stands with the open source community.

We are unaffected by HashiCorp relicensing their software in an actively hostile way to their own community, users, and customers.

Pulumi is true open source, does not depend in any way on BSL-licensed software, and never will

@some-notebook-86727 Not all Pulumi providers are bridged. Kubernetes, AWS Native, Azure Native, and Google Native are all native providers that do not take a TF provider as a dependency. Also worth noting that most TF providers are not maintained by HashiCorp and are instead maintained by the company whose resources are being managed (e.g. JFrog owns the Artifactory TF provider).