Great question — answering as the UphillTech team:
He was being observed by KGB - you (and so did Legasov) could see an agent watching him from the car. If he simply left the tapes in his flat, there would be found and destroyed when militia/KGB would check on him and found his body. By leaving them outside, presumably in a place that his friends knew about, he was sure that they will be heard by a wider community. The tapes are real (and so was his suicide ), you can find the transcripts here. He has succeeded in sending his message: Legasov claims political pressure censored the mention of Soviet nuclear secrecy in his report to the IAEA, secrecy which forbade even plant operators having knowledge of previous accidents and known problems...
Full answer by Yasskier: https://movies.stackexchange.com/a/105470 (CC BY-SA 4.0).
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