When an existing project is opened from a location where it hasn't been created on that machine, the Editor is unable to parse the project's location properly and fails to show it in the Project Browser UI that appears when the Editor is invoked without a project.
It seems that UEditorSettings::RecentlyOpenedProjectFiles was changed from an array of strings in UE4 to an array of FRecentProjectFile structs in UE5. However, the Project Browser doesn't use config object serialization to read this list. Instead, it directly reads the property from the INI file in DesktopPlatformBase.cpp, which now causes it to construct an invalid path from the serialized FRecentProjectFile object representation.
There's no existing public thread on this issue, so head over to Questions & Answers just mention UE-170187 in the post.