Oh, the command was:
/give @s iron_axe[minecraft:can_break={predicates:{blocks:"#logs",show_in_tooltip:false}}]
I just wrong the later command and it worked as expected, able to break only logs in adventure mode while fully hiding "Can Destroy". You may now deem this issue invalid if necessary.
/give @s iron_axe[can_break={predicates:[{blocks:#logs}],show_in_tooltip:false}]
Was I just typing the command wrong the last time?
Oh, the command was:
I just wrong the later command and it worked as expected, able to break only logs in adventure mode while fully hiding "Can Destroy". You may now deem this issue invalid if necessary.