What effects, if any, interact with the druid's Timeless Body class feature?
Timeless Body is what Wizards of the Coast has called a "Ribbon", i.e. a neat ability with mostly story, rather than mechanical, applications. Another ribbon ability is the rogue's Thieves' Cant, though that has more obvious benefits to the campaign at large.
See the sidebar in the Waterborne Adventures UA article here for a full explanation.
I can't think of many things that interact mechanically with timeless body. It wouldn't be unreasonable to rule that it also reduces aging from various mechanical effects, like Wild Magic Surges or potions of longevity, but aside from those edge cases, which are arguably subject to ruling anyway, the ability's mostly for fluff.
In story, I can see it causing very old archdruids running around the setting.