There is no paid plan, no card, and no quota. OMEM is early software and what it needs right now is people using it and telling us where it breaks, which is worth more than the revenue a product at this stage would make.
Self-hosted. Runs on your machine with no account anywhere.
When that changes
The reference engine and the SDKs stay free and self-hostable regardless. You should never pay to define what a memory means. If a hosted service is ever charged for, it will be for running it at scale, and it will be announced before it is billed, not after.
What OMEM does not have yet is on the security page, and it is worth reading before you plan around it.