The best solution is to place the library on a shared exFAT partition, as exFAT is a case insensitive file system. So no need to worry about case-sensitivity problems when using Calibre on Linux or Windows
Just to justify it for those who encounter a similar issue or are simply curious, as I am discovering all this through experience. I had Calibre installed on Windows, with the library stored on a shared partition accessible by both Linux and Windows. Originally, this shared partition was formatted as NTFS, and I tried to install Calibre in Linux using the existing library, but Calibre warned me about potential risks related to case-sensitivity issues, so I didn't do it. Then I reformatted the shared partition to exFAT, and when I installed Calibre on Linux again, it no longer warned me about any potential risks. I have tested this setup extensively and haven’t encountered any issues, such as "book not found" errors or similar problems.
It seems that although NTFS, like exFAT, is a case-insensitive file system by default, when an NTFS partition is mounted on Linux using the ntfs-3g driver, it can behave as case-sensitive in certain scenarios. On the other hand, exFAT has native support in the Linux kernel (since version 5.4) and does not rely on an external driver. While tools like exfatprogs may be required, they act as administrative utilities rather than a driver.
An exFAT partition mounted on Linux functions fully as a case-insensitive system, avoiding the case sensitivity issues that can occur with NTFS under Linux.