Pulumi is free: "Pulumi is true open source, uses the Apache 2.0 license, and does not and never will depend on BSL-licensed software in any way, HashiCorp owned or otherwise." (https://www.pulumi.com/blog/pulumi-hearts-opensource/)
Pulumi Cloud (the SaaS offering) is (mostly) not free. There is a free tier for individuals/companies with minimal needs.
You may happily use Pulumi and manage your own state files, for free, and open source.
I yet have to read/hear about somebody self-hosting Pulumi. It lacks the huge Terraform ecosystem and without the paid cloud offering, it's pretty rudimentary.
It is possible to self-host it on GCS, S3, etc. We used to pay for their cloud offering, but using GCS as a backend was much more performant than using their backend and extremely cheap (a few cents to dollars per month).
I've had a disastrous experience with Pulumi several months ago trying to set up some basic Azure setup - it wasn't anything like Terraform, so, I switched to CDKTF for that, and it was nice except that I first attempted using Go, but, ideally, it went with TypeScript as it was significantly more ergonomic.
Pulumi Cloud (the SaaS offering) is (mostly) not free. There is a free tier for individuals/companies with minimal needs.
You may happily use Pulumi and manage your own state files, for free, and open source.