This issue has only started today, yesterday when I got the Neptune's Bounty everything worked, and I got my reward.
Today, I got 3 Neptune's Bounties and in each one of them I got nothing.
Is it just me being very unlucky, or is it not supposed to happen?

Neptune's Bounty should always contain something when caught.

Have you caught it with a fishing rod, or used some kind of fishing trap/auto fisher mod?

The modpack I'm playing is using version Aquaculture-1.16.4-2.1.12.jar

Thanks for the updated video!
Is the modpack publically available by any chance?

Yes, here's the link: https://www.curseforge.com/minecraft/modpacks/epsilon

I caught it with a diamond fishing rod from aquaculture.

What version of Aquaculture 2 are using?
Also, could you provide a video of you showing the tooltip of it, before placing and opening it?

Unable to reproduce the issue using Epsilon

Are you playing singleplayer or on a server?

That's your problem then. Any of those Bukkit/Forge hybrid always causes a lot of issues, and there is never anything the mod can do about fixing the problem.

Yes, I am playing on a server. Is the mod not working well with Mohist 1.16.5 or any of these plugins?