I’m very sorry for your losses.
Young bunnies are very fragile. They can get diarrhea from a parasite (coccidia) or bacterial overgrowth in the intestines because their GI microbiota isn’t fully developed, esp if they were weaned very young.
That the 2-year old bun also got watery diarrhea is more difficult to understand. It’s not a common thing in adult bunnies. You often see sticky poop, but that’s never watery, just sticky or loose. The rescue gave you appropriate advice for dealing with sticky poop. There’s always the possibility that bad bacteria managed to colonize his gut and that led to diarrhea and his demise. Rabbits’ guts are sensitive to stress, and getting a new home is stressful – even if it’s in a good way, it still can upset the system.
Chuck out the timothy in case it was compromized in some way, clean everything with 10% chlorine bleach or Virkon S (a disinfectant for horse-stables originally, but very useful for people with house bunnies because it’s non-toxic, doesn’t stain or smell). Wash fabric toys and blankies in sth like 140 F or 60 C, and you should be good.
Rabbits are fragile and can go downhill really fast, so diarrhea always requires emergency vet care.