With your own AI key, your provider charges you directly for what the AI features use; 1kr doesn't charge anything for Starter while it's free.
How much: each provider's cheapest models are used, so a 1krBlocker Deep check costs a tiny fraction of a cent. A 1krNote voice chat costs more, because live voice is priced by the amount of audio. Exact prices are on your provider's pricing page.
Free tiers: Google's Gemini API has a free tier with daily and per-minute limits, often enough for personal use. When a limit is reached, the provider refuses requests for a while, and the AI features stop working until it resets. OpenAI's API is paid from the first request.
Keep costs under control: set a monthly budget or spending limit in your provider's console (Google AI Studio or Google Cloud billing, OpenAI's usage limits). The apps also have their own daily caps.
Privacy: Your provider processes the redacted text under your own terms with them. Free API tiers may let the provider use it to improve its products.