Unfortunately, copying tracks between Soundtrap projects is not directly supported at the moment. Check out some of the possible workarounds below.
a) If you just need to duplicate the project, this is done by opening the project and choosing "Save as.." under the File menu (1). (This is also super useful for alternative versions, or backups when you go wild with experimentation.)
(1) File menu - Save as..
(2) Save as... dialog
b) Export the track you want to copy between projects, and then import the downloaded file into the new project. Click the dot-dot-dot in the track header (it appears when you hover) of the track you want to copy, and select "Export this track" (3). For MIDI/instrument tracks, this option will be called "Export as audio file".
(3) Export this track
c) If it is a region that you want to copy, consider adding it as a loop to the loops library. That way you will get access to it from any project! Your own loops are private, so they will only appear in the loops library for you and not for other Soundtrap users. Hover over a region and click Edit (4), select "Add to loop library..." (5) and in the dialog, enter the details that you would like to save with your loop (6).
(4) Hover over the region and click Edit
(5) Add to loop library...
(6) Enter a name for your loop, choose tags (you can choose as many as you want) and click Add Loop to add it to your loop library.