There’s a few techniques that you can use depending on the limitations you are willing to accept.
The more Dynamic the final thing needs to be the more complex the whole setup will be.
As far as i am aware mudbun is sorta voxel based so making that from scratch will take a while.
If you need something that is static, Unity supports VATS (Vertex animation textures) and Alembic.
Alembic is a Geometry flipbook and can quickly get super expensive in terms of resources, however each frame can have its own set of vertecies, so you can have a glas filling up or a volume growing etc.
With VATS your limited to a set amount of Verts that can’t change in number and you are limited by the Texture size it reads from but its a shader based solution and comparitively cheap. You can Animated a mass of Crowds with this technique easly.
EDIT: I think looking at the gif really derailed my idea of what you want into something very complex.
I want to make a gooey splash that lasts for about half a second
I’d recommend just using particles honestly. You can use a normal map of a sphere and distort it to get wobbly looking droplets. you can also use a single ‘frame’ of a fluid sim of a splash in blender to make a non-animated splash mesh. Find the nicest frame of that sim, and export just that mesh. decimate it, and distort that with shaders to make it wobble and scale it over time.
Sorry to state the obvious off the bat, but your post was a bit ambiguous - Mud Bun is a Unity plugin.
But I will assume you mean without the plugin. This is a pretty complicated effect (3D water is one of the hardest things I’ve had to do in games, and I spent a year trying). @Ganishka’s response here was spot on. I’ll elaborate a bit further with some links:
For something more static, like the player splashing into a pool of water, VATs can make it look really nice. If you have access to houdini, there are a lot of resources to search for and you can use Keijiro’s plugin. If you don’t, then you can use Gaxil’s Alembic to VAT tool.
If you really need a volumetric looking effect like mudbun, you could investigate Clayxels, which is simlarly priced, but I think both plugins go on sale.
You could also do it in screen space using a render pass like in this Unity example project, however this get’s pretty technical with render passes.