1. Open Settings > Advanced (the gear icon, then the "Advanced" tab).
2. In the search box at the top, type "Prevent control sequences from changing the current profile".
3. Set that option to No.
You're right that it doesn't use semicolons as separators between the parts. The actual format is:
ESC ] 1337 ; SetProfile=ProfileName BEL
or written out: \033]1337;SetProfile=ProfileName\007
There is exactly one semicolon, the standard one right after 1337. After that it's a single key=value pair (SetProfile=ProfileName) terminated by BEL (\a) or ST (ESC \). So unlike OSC sequences that take multiple semicolon-separated arguments, this one has no internal semicolons. A quick test from the shell:
printf '\033]1337;SetProfile=Default\007'
Replace Default with the exact name of the profile you want to switch to.