Without knowing what OKR is, things are getting a little difficult to respond.
But for now it will assume it is just another survey and ignore whatever OKR is.
Goals of the survey - LimeSurvey
One place for OKR set owners to update grading results and add OKR reviews each quarter to simplify the process and improve adherence.
Automatic statistics created by LimeSurvey show participation, grading result averages by department/all and lessons learned from the OKR cycle, transparently available to everyone.
I think "response rate" often has little to do with the tool itself, rather with the way this has been setup. I don't know Confluence, so I can't compare or say where their strength and weeknesses is.
I think to get response rate up, creating a good process and flow, as well as awareness of the importance within the organisation is far more important than to use tool X or tool Y.
Of course, some tools can support you in creating a better experience.
I am not quite sure, what the actual question is, because I don't really understand the setup and the requirements your "OKR champion" has (those titles are getting more ridiculous every day...

).
Limesurvey's inbuilt reporting is rather basic, in my opinion. However, I don't know the benchmark "Confluence", so difficult to judge. Maybe it is already enough for your needs (which we don't know).
For deeper analysis you still need to use a tool specialized on data analysis (SPSS/PSPP, STATA, JASP, Excel, Google Sheets, whatever).
To be honest, reading the description, I think the situation will not change with a different tool, I think the internal processes will need to be revised.
But if you can give us an example of how such a OKR evaluation looks like and how the analysis should look like, we might be able to give you some more feedback on how this could be done in LImesurvey.
Through the API and some Addons and or direct access to the database you probably can built a pretty good tool for that.