That said, if we have a very liberal definition of the word "website" to include any successor technologies where a device can be used to request a document, given an identifier, that looks recognizably like your webpage, this is doable. What you really need is an institution that you can trust to keep existing and to keep the necessary upkeep of your website as part of its mission.
The main institutions I can think of that have lasted for 500 years unbroken are churches and elite universities. If you were able to convince the Pope to decree that the church should keep hosting your webpage in perpetuity, that would likely work, but persuading him of that sounds very challenging. That said, universities are used to accepting gifts with sometimes eccentric strings attached. The gift will probably need to be large; but I imagine a $1B donation to Harvard under a condition that they continue to host and update the page as needed would likely work. Getting that sort of money is quite hard, but tbh probably easier than coming with a way of guaranteeing that your direct descendents keep the webpage up.