How to save the full path when importing an image file?

It depends on whether you are using Lightroom in Cloud or Local mode.

If the Cloud tab is selected, there is basically no local path because all originals get uploaded to the cloud. The only local path is in the originals cache, and whether an original is actually there depends on whether the cache has room for it.

If the Local tab is selected, you’re working with photos on your local storage. You can make any folder a Favorite, so that you can quickly get to it later in the Favorites tab when you want to use that folder for projects and further organization.

If you mean you want to be able to retrieve the full folder path as text you can copy and paste, I’m not sure if that’s a current feature in Lightroom. But that feature is available in Windows Explorer, so if you’re using the Local tab in Lightroom, you could right-click an image, choose Show in Explorer, then when the computer switches to the Windows desktop with that file selected, right-click that file and choose Copy As Path. Now you can paste the path text somewhere else.