If the security and anonymity of your merchant website are your concern only BTCpaysever is the only option.
And add more privacy/anonymous coins like XMR or you can accept only Bitcoin and later use a mixer to receive clean coins.
And I'd like you to suggest it is easier to implement if you use CMS like Wordpress for your digital marketing because BTCpay is easy to setup there based on my experienced.
Also, BTCpay is self-hosted you need to host them with your own either in your PC or server.
the BTC you receive on BTCPay are automatically converted if I remember correctly.
Actually, it's not auto-convert it only automatically sends to exchanges and sells immediately but it seems they don't implement it yet according to
this.