When I connected a single LED to the output terminal there was no problems at all so I assume the size of the rope light means that another approach is required.
Here is the setup:
The USB power is 5V.
Tasmota 8.5.1
FYI: I soldered the red / black wire the wrong way round.
Usually you just add the power requirements found in the product specifications.
I just had a look at the sonoff website and this is not published for the SV. A quick search online revealed this to be 150mA peak and 20-40mA average.
So that just leaves your LED lights. Do you have any data for them?
You could check the voltage of the 5V power supply when trying to turn it on. Also if you still have the battery pack you could measure the current drawn by the LEDs.