As long as your trust set-up is sufficiently well-funded and well structured the trust could in principle live on for generations. Obviously, the success of the venture depends on, well, trust.

The trust structure would have the obligation to maintain the website. Provided they make backups, which is totally a thing you could write into the contract (every five years a lawyer copies the site onto whatever document storage system they're using at the time, or puts a new tape in a safe), that would outlive any individual company.

There are however legal rules against trusts in many jurisdictions: https://centaur.reading.ac.uk/100782/1/Article%20-%20The%20r...

So your best bet is to establish a community of people interested in preserving your website, or websites in general, and have them run a long term nonprofit for that purpose.