When I export to save a photo, the saturation somehow increases after saving

It means you are looking at the exported file using an application that is not color managed. The main photo viewer in Windows is not color managed for example. It means that the application does not take into account the color response of your monitor and just sends the image data straight to the display without correcting it. This is a problem as many current computer monitors are what's called wide gamut, which means they can display much more saturated colors than the internet standard called sRGB. If you run unmanaged applications on such a system, you will see oversaturated colors if you export your images to the default sRGB color space. Lightroom is color managed and does the translation for you and will show you the right color if you for example reimport the exported image. Also Photoshop and many better photographic applications are color managed and will show the right colors. In some programs you have to enable the color management in their preference settings. This problem is very common on windows machines where historically there has not been much color management in most applications. Luckily finally most browsers even on windows are color managed but many system utilities still are not.