A few options: grab a VPS from a provider that accepts Bitcoin (Njalla, 1984.is, Bitlaunch), pay over Lightning for better privacy. Run it behind Tor or a VPN you trust. Use a dedicated npub that isn't linked to your main identity. For the API keys (Anthropic etc.), you could buy prepaid credit cards or use privacy-focused payment methods. The main leak vectors are payment trails and IP, so focus there.