For example, let say someone has registered a meta-analysis in PROSPERO back in 2018 but the study is not completed even in 2022. So, in such case can a different person conduct the same meta-analysis on his own? What do the research ethics says to this?
Yes. I believe that the main goal of registration in PROSPERO is to provide a version of the systematic review protocol, hopefully prior to data collection and analysis, that readers of the eventual completed systematic review publication can use to check whether undue deviations were committed for whatever reason. Such registration is hoped to stem publication/reporting biases.
While one of the stated goals of PROSPERO is to "help avoid duplication" (https://www.crd.york.ac.uk/prospero/#aboutpage), I think that this is not necessarily the same as staking a claim on a systematic review topic. Replication of studies and findings is an important endeavor on its own in original research, and I think that it must also be the case for systematic reviews - especially since there is substantial subjective component in systematic review writing. It would always be interesting to see agreement or disagreement between systematic reviews of the same topic, finding out where the agreement/disagreement lies in the body of the reports, and make a research or practical decision based on these. People may arrive at the same topic, but the execution of the review (including the articles included and excluded) and the quality of the written output will most likely differ.
For the sake of formality and courtesy, you can consider getting in touch with the PROSPERO entry's corresponding person to ask for an update on their review.
I agree with @Aedrian Abrilla's suggestions. In addition, it is better to request the corresponding author(s) about the reason of delay in publishing report, expected date of completion, scope of joining the SR team etc.
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