Probably it should be replaced with parseAsContent, but that's only available in 1.32.
During testing Niklas found that that external link icon disappears when this patch is applied.
I did some digging regarding this and I've documented findings here - https://www.mediawiki.org/wiki/User:APatro_(WMF)/OutPutPage::parse
Output from parse is wrapped in a div tag with class mw-parser-output whereas the output from parseAsContent is not.
I think it is expected for the parser content to be wrapped inside a container with .mw-parser-output class. Hence updated the patch to add this.
During testing I also noticed that the editable documentation does not have the mw-parser-output class either causing the external link icon not to appear there either.
@Nikerabbit - Would you like me to file a task to fix this?