Steps to reproduce:
Give yourself any potion effect
Mount a horse, strider or pig
Observe in the top right corner that the potion effect is displayed
Open your inventory and see that there are no potion effects shown
This is also inconsistent with the Nautilus, where it works and all potion effects are correctly displayed even when mounted.
For demonstrations, see the attached videos.
Thank you for your report!
We're tracking this issue in MC-19974, so this ticket is being resolved and linked as a duplicate.
That ticket has already been resolved as working as intended, which means this is not considered a bug and won't be fixed. Please do not leave a comment on the linked ticket.
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