My work permit is about to expire and I have yet to apply for express entry. I have 3 years of work within Canada and will be applying for visitors visa to extend my stay.
Am I still able to apply for express entry under visitor visa?
Create your EE profile and wait for an invitation. Once you receive ITA and submit your application I think you can apply for BOWP but I'm not sure about it. You'll have to wait for other opinions from people who are smarter than me in this regard.
You should create your express entry profile right away. I am pretty sure you will get an ITA in the next draw based on your experience in Canada. If you have already taken the IELTS or CELPIP you should be good to go.
If you are able to get police certificates from you home country soon enough, you maybe able to complete your application and submit within 39days when your PGWP expires. If this happens, you should be able to apply for BOWP and continue working until you receive PR status.
Check your projected CRS points in the following link and check if you receive about 425-450 points. If yes, everything I mentioned above maybe possible without having to apply for visitor visa.