TLDR: I think the 4-5 weeks is only applicable to the first next update, after that no fixed time for the final results, which MOE always stress in their email "Please note that this notification is not intended to create any legally binding obligations and that the matter is still subject to contract."
If this is the first time you are applying for govt jobs, they always have long processing time. MOE is probably the longest. Just like what your friends have said, for some sectors, your application might just be at processed for 6 months without telling you that you have failed. At least from what some had said previously, no news means you are still being considered and MOE will always tell you that you are rejected, when you are rejected.
And every application will be different. My status was only changed to shortlisted 2+ months after the interview (after they ask me to change my 2nd teaching subject), while I have another forumer who already got shortlisted for the same 1st subject.
Even before covid, you won't receive your application RESULTS by 4-5 weeks, but you might get a update like asking for EPT date (I think the 4-5 weeks is only application to the first next update). And if you don't have to take the EPT test, you have to wait for others that are taking, so judge the amount of time to you have to wait for the next update. In other words, treat it that they go through the different stages for all applications as a whole.
Last year after the end of my interview, like when I was packing my stuff, my interviewers asked me if I am still applying for other jobs (which I said no), after that I sort of understood that the waiting time will be longer than expected. If you are anxious to get a job and have other job offers, depends on your feel of your chances and your feel of becoming a teacher, you can consider applying for other jobs (although I didn't and waited for 8 mths). You can always quit your job if the offer does comes or delay your MOE offer (take note of resignation notice period).
If you decided to wait, don't need to stress yourself by refreshing the career@sg page everyday/hr xD, just check every few days, turn on your phone notification for your email account and enjoy your semi-holiday