Locally ran?

I have seen posts about being able to run supabase's CLI locally. I'm pretty new at this stuff, I'm just wondering if I run the database locally... do data rates apply when storing data to a local database, meaning like can i essentially run supabase free by running it locally? I fully intend to run the site locally then move to a data store facility if it came to it but I'm a little stumped, I have a whole social media platform and I rather it be ran locally than on a online platform where it's harder to monitor IMO
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