In versions before 1.20.5/6, it was possible to hide the tooltips for potion effects using HideFlags. The bit that controlled this was value 32, or the 5th bit. I believe this bit was changed to stored_enchantments.show_in_tooltip when the 1.20.5 update happened, and now, changing this field no longer hides potion effects. Setting every possible toggle using the "toggle_tooltips" function does nothing as well, so it appears that hiding potion information is no longer possible.
To Reproduce:
/give @s potion[potion_contents={custom_effects:[{id:speed,duration:300}]}]
Hold the potion in your main hand
/item modify entity @s weapon.mainhand {function:toggle_tooltips,toggles:{attribute_modifiers:0b,can_break:0b,can_place_on:0b,dyed_color:0b,enchantments:0b,stored_enchantments:0b,trim:0b,unbreakable:0b}}
Notice that while your potion does indeed now have lots of components specifying tooltip visibility, the potion effect information is no longer hidden.
A surface-level fix for this could be to make the stored_enchantments flag also hide potion effects like it did before, but perhaps a better way would be to add a show_in_tooltip field to the potion_contents component.
There's a separate component for this called
hide_additional_tooltip