What does a systematic review entail? In what way is it "tedious"?
Tedious has a negative connotation. In many ways systematic review is meticulous, which to some people may appear tedious. One who enjoys reading, inspecting clues, and putting puzzles together to reveal hidden patterns would enjoy doing a systematic review.

The first hurdle is perhaps setting up the research question and search criteria. If the set of keywords is not close to perfect the resultant articles may not be exhaustive, and being exhaustive is a spirit of systematic review. In addition, all searches need to be documented through writing or using codes, so that the search can be replicated by other people.

The second hurdle is combing through moderate to large amounts of abstracts in order to identify the right targets. A set of carefully developed selection criteria will help. But a good handful of the retrieved abstracts may still fall into the gray zone and require some meetings to sort them out

Then it comes the actual reading and data extraction. This can take months and months of reading, re-reading, tabulation, and revision. Again, if the authors know what to extract very clearly, the process can get less iterative.

Notice that for the previous two hurdles, some research team may require two or more researchers to do them independently and then compare their results for agreement before divvying up the work. Be prepared for frequent team meetings or communications for troubleshooting.

The last hurdle is to put all the tabulated information into use, through grouping, sorting, summary, and synthesis. This requires a great deal of understanding from the reading process and one's experience. The process can often be iterative. Making a good conceptual framework will help setting up a more robust draft. Keeping the research questions in mind as the north pointer can also prevent getting lost.

And, all of the actions above need to be documented so that anyone can pick up the review and conduct a similar search (say, maybe 5 or 10 years later) in order to compare with what you found. In a way, systematic review can be viewed as an exhaustive, planned, and replicable literature review.

Now back to your case. If it's 10 hours a week for a semester, chance is you will not see the fruition of the article, but you can definitely take part. The important part is to get a very clear idea which part of the process you're taking. Article searching and downloading may work for more flexible schedule, even 10 hours on a day per week is fine as long as you keep good searching notes. But if it's the later stage, it's better to work on it by small amount, like 2 hours every day, as the later stage requires more consistent immersion and regurgitating.

And if I may make another suggestion, ask if the supervisor needs anyone to do a more general literature review for a grant proposal or a journal article. That should give you a smaller, more defined task and you can use this chance to see if you like this kind of work and, more importantly, if you and your supervisor work well together.