这种情况大概率是在 fstab 挂载的时候忘记加 exec 参数,导致 steam 无法创建 sh 脚本并运行导致的,将外置分区挂载添加 exec 参数即可解决。

打开/etc/fstab,往你的挂载分区参数里加上 exec 参数即可,推荐加载所有参数后面。

/dev/sda4                                   /mnt/linux-hdd          ext4    nofail,users,exec                                                                                       0 0

Cannot add library folder because of missing execute permissions

Make sure you are mounting the filesystem with the correct flags in your /etc/fstab, usually by adding exec to the list of mount parameter. The parameter must occur after any user or users parameter since these can imply noexec.
确保在 /etc/fstab 中使用正确的标志挂载文件系统,通常是通过将 exec 添加到 mount 参数列表中。该参数必须出现在任何 userusers 参数之后,因为这些参数可能意味着 noexec

https://wiki.archlinux.org/title/Steam/Troubleshooting#Cannot_add_library_folder_because_of_missing_execute_permissions