Nitpicking, but to be clear, by STR, I think you mean SRT - the common sidecar caption/subtitle file?
If you use a Word document, be sure to "save as" a text document (.txt). Word is known for introducing invisible characters that will mess up your captions.
Before I describe the method you requested, I recommend that you actually just create the new translation in the .srt file being very careful to keep the caption numbers and timecodes exactly as they are. "Save as" that file to a new name. If you use Word (e.g. for spell check), do a "save as" to a text file and then change the file name to .srt.
In PR, click on the eyeball in the original caption track HEADER so it is disabled. In the Text panel, pick "Import captions from file." Navigate to your new srt file. In the "New caption track" dialogue that appears, Set it to the same caption type as your original (608 or 708) and for 608 set to CC2 and for 708 set to Service 2. Leave the default "Source timecode" and click OK.
You should be good to go!
There may be times where you need a different method. For the method you requested, Do NOT copy the timeline (sequence). That does not create a second caption track in the SAME sequence. That is ultimately what you want. If you use a separate sequence, no matter; you can copy paste a caption track from another sequence just as easily as I describe below.
COPY the caption track in the original sequence. (In my test, I started with a single 708 track.) There is no duplicate command for captions, so I think the easiest way is to use the "\" key to show your entire sequence in the timeline. Then drag-select all the captions. I would start the drag from the end - too hard to start at the beginning. Ctrl-C to copy. Right click on the caption track header, and pick "Add Track." Set to 708 Service 2. Set the CTI (cursor/current time indicator) to the start timecode of the first caption. Ctrl-V/Paste.
Now edit those captions.
Note that you can see only one caption track in the Program Monitor at a time. But when you export and embed captions you get all the tracks. There may be some gotchas there, so be sure to test your whole workflow before you do the whole thing.
Additional questions are whether you actually need to embed closed captions or need both 608 and 708 caption types.
Stan