I'm not familiar with this issue, but I'm certainly interested.
When I mentioned above that Arduino IDE 2.x has better support for the src subfolder, I was referring to this bug in the classic Arduino IDE:
"Save As doesn't preserve the src subfolder of the sketch folder"
That's the only change I'm aware of related to the src sketch subfolder.
But it doesnt' really seem related to what you described. When you use the double quotes #include syntax, the local path should always be searched first for the file, only checking the global libraries paths if it's not found there. I've had problems with bundling standard Arduino libraries with sketches in a couple of cases:
The library unnecessarily used the angle bracket #include syntax for local files
Even though this is incorrect, it does no real harm when the library is installed normally, but these don't work when the library is bundled with the sketch. So I had to go into the library and change all the angle braces to double quotes.
Using multiple sketch bundled libraries that have dependencies on each other
It is correct to use the angle braces #include syntax for header files in other libraries, but the src subfolder of the sketch folder is not in the include search path so these files won't be found. In this case, it's not only a matter of changing the brackets to double quotes. You also need to provide the relative path to the file in the other library.
These are a little inconvenient, but only take a few minutes to make the simple fix.