New info and (partial) solution
After the input from Markus von Broady's answer, I took a different turn on my project to account for the attributes limit in the shader editor. For this, I had to rearrange the way I was making my mesh so that the inputs that came from the geometry nodes to the shader editor were not all compacted in a single material but spread through various materials, each one not exceeding the supposed 14 limit per material.
Meanwhile all this, I also got an idea ((not a new concept but)) for virtually increasing the max number of attributes by 4 times. This is done by compacting 3 values/attributes all in one vector or a color and then unpacking them on the shader editor. Color has 4 floats instead of 3 (R,G,B, Alpha) but as in per 4.1.0 alpha the Separate Color node has alpha channel only on Geometry Nodes but not on the Shader Editor, which means you would be able to compact it, but then not to extract the 4th value in the alpha channel. EDIT!: Later after this post I freaking realized you can actually unpack the alpha channel, so you can use 4 slots. Its not through a separate color node but directly through the attribute node which has an alpha output in itself (how didn't i see that lol)!
Demonstration [old method using vector, color is better with 4]:


Anyways, so, with this method I was having the materials in my mesh with only like 3 attributes or less each. And everything was going fine till today, when some of my attributes started not working again, even tho I'm not exceeding the limit per material. I did some testing and turns out the limit is (EDIT) 14 only when you have no Texture Coordinate node and 13 when you do (12 if you use Generated - because I think it uses the 2 vectors that make up the objects bounding box)... and it isn't per shader, but per object. Yeh....
Summary
I'm gonna do a list of basically everything I know now about attribute limits: (I tested this both on 3.6.2 and 4.1.0 alpha.)
- Like Markus tested you can have hundreds of stored named attributes per geometry node and that isn't the problem.
- You can only receive a max of 14 attributes per object on the shader editor, independently of how many shaders they are spread on.
- Having multiple geometry nodes in the object storing different attributes doesn't change anything, still the total max per object in the shaders is 14.
- If a shader has more than 16 attributes, it will literally break and turn pink (only that one, not all in the object).
I'm leaving the .blend file in case people wanna test it out in the future.
I wish the devs would increase this limit in the future updates tho...
