Thanks Corley. It just seems that matching on the new tree is stuck in limbo somehow. When I've re-uploaded my tree in the past, I'm sure that record matches and smart matches have populated fairly quickly. I've even tried making a few edits to my tree in the hope that it might kick-start MH's routines (whatever they are) into running through it.
Strangely, around the same time (17th October) MyHeritage hints stopped working in my Family Historian software. Every time I open the program or open a project, I get a notification after a short time that "The MyHeritage service has been stopped. Too many errors".
There are other similar reports on the Family Historian User Group forum, but it isn't affecting everyone, and there seems to be no obvious pattern. Calico Pie (the FH developers) have a notice on their website saying that the problem relates to a DNS routing issue affecting some users, and that they are working with affected ISPs to resolve it. I find that odd too, as others using the same ISP as me seem unaffected.
It suggests to me that something more fundamental may be wrong at MH, but I'm far from an expert. Hopefully posting this will prove me wrong and I'll find everything working again in no time!