Ideally you need to get on to the hosting company and explain and see if you can take over the account, if you can do that you can rescue the whole database but obviously would be far easier with family contact, I have recently done the same with Trevors (Vetchugger) normanboats.co.uk website to save all the old info and forum but I had the massive advantage of knowing all the account details and passwords already and found his son through faceache to get the go ahead, I just had to pay the outstanding bill that was due when he passed away.
Hosting details can be found here.
https://whois.domaintools.com/broads.org.uk
20i.com seem to be the hosts so may be worth a call if only to get them to save the database to give you more time instead of just deleting when the account expires, the domain is shown as available so I guess expiry is very close or passed. Edit: 16th may 2021 it seems.
As for mediawiki, never heard of it.