Most tabs are closed, and that is the default
TikTok ships with the Liked list set to private, and changing it takes a deliberate trip into privacy settings that most people never make. So an empty result here is the normal case rather than a sign something broke. There is no workaround: when the platform does not publish the list, nothing can read it, and any tool promising otherwise is either guessing or lying.
You are downloading someone else's upload
A like never creates a copy. The file you save belongs to the person who posted it, at the resolution they uploaded, with their handle in the filename. That matters if you plan to repost anything: credit follows the original author, not the account whose tab you browsed. For personal reference and offline viewing this is rarely an issue, but reuploading someone's work without asking is still their call, not yours.
The list moves as they keep watching
Liked tabs are ordered newest first and shift every time the owner hearts something else, so the same profile can look different an hour later. If a clip matters to you, save it when you see it rather than bookmarking the position. Unliking removes an entry entirely, which is another reason the tab you loaded yesterday may be shorter today.