In principle, you should only conduct a systematic literature review (SLR) if:
- none has already been done recently;
- the only ones recently done are deficient in some way (that you will clearly explain and correct); or
- you adopt a very different perspective that adds something significantly valuable that is different from the recently published good review (e.g. you do a meta-analysis, unlike the other review; or you deep-dive into a specific subset of the literature that the other review covered only briefly).
In general, unless the recent review is quite bad, I think that the third option is the only good justification for publishing another SLR on the same topic so soon. Note: I am talking about justification from the journal editor's perspective of why they would agree to publish your review; you have to think in this way whenever considering getting anything published. Moreover, the third option is the safest, since you don't need to offend anyone by trying to make up bad stuff to say about the recent review to give the impression that yours is better--you only need to prove that yours is valuable in a very different way, not that it is better. And finally, the third option might sometimes be easier because you definitely should not duplicate the work that the recent review has already done--rather, when you find your own unique perspective or approach, you should spend all your time and effort on only that.
But if you cannot find a new, valuable perspective to adopt and the recent review is quite good, then I don't see anything for you to do other than appreciate their review and thank them for saving you from having done all that work yourself. Of course, in that case you would have no standalone literature review article to publish, but you could probably salvage the work you have done so far as bits and pieces of other related research that you may do.