When a Life Cleric activates an item that can restore HP—like the Staff of Healing—that expends charges to cast spells without consuming spell slots, Disciple of Life should not add extra healing. The feature specifies that you must use a spell slot to receive its benefit.

However, on D&D Beyond, the item shows the benefit of Disciple of Life to each spell. Was there an update to the 2024 rules or errata that changed this, or is this a mistake on D&D Beyond’s part?

The Disciple of Life feature was very difficult to code in, taking years to do it (admittedly a lot of that was prioritisation/time). That was the 2014 version which does not require a spell slot - just any healing spell so it did indeed work with items.

The 2024 version requires a spell slot but this would be even more difficult to code in and would need to be an entirely separate version. 

So it is a bug for 2024 Life Cleric, not a bug for 2014 Life Cleric, and is not likely to get fixed any time soon. 

Honestly, it's not broken at all to let Disciple of Life work with items and such. The only reason for the 2024 update was to prevent exploit using Goodberry (since, by RAW [as confirmed by rules designer] it meant each berry healed 4 hp instead of 1, so 40 hp healing for level 1 spell that you could cast for free using Magic Initiate) or persisting healing effects like Healing Spirit. As long as you watch out for those, adding Disciple of Life to Staff of Healing doesn't create any balance issues.