We've been using a 9361-8i in a SuperMicro server since October 2020 with ESXi 7 and now with ESXi 8. It isn't clear if you already have your 9341 running in an ESX 6 system and want to upgrade it to 7, or if you're building a new ESX 7 system from scratch. If the latter, you need to make sure the card is in a supported PCI slot. Also when the machine boots you should see the 9341 initialising at the bios/efi stage, and also get prompted to configure it and any disks if desired.
On our ESXi 8 system the 9361 shows as a Broadcom MegaRaid SAS Invader device - I can't remember what it was listed as prior to the ESX 8 upgrade. We didn't install any specific drivers for it - I understand that ESX has built-in support for the card. I can't comment specifically on the 9341-4i except to say that we used one in an earlier ESX machine prior to Oct 2020, but that was also ESX 6.7U2 then. We did take all of the disks that we were using with the 9341-4i and the raid configuration transferred over to 9361-8i, which was a real bonus.
We use storcli to manage the controller in the ESXi shell environment.
