Maybe you mismatch drivers from the RAID controller. 

To be honest most of the time - Servers are coming already with a mounted RAID Ctrl. And for ESXi installation we are using vendor customized ISO.

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.

Does that mean that the LSI MegaRAID 9361-8i is in fact compatible with ESXi 8u1?  

I need to update my RAID controller before I can build a new ESXi 8u1 host, but I'm having problems finding the exact model on the HCL.  I realize I may need to update the firmware, but just wanting to verify that it's on the HCL for now, before I make the purchase. 

I've been away on leave....

I haven't done the 8u1 update yet, but I'd assume that if it works fine on 8 it should be fine on 8u1. The HCL does list Megaraid 3108 controllers under the LSI manufacturer, and in that list Avago is shown too.

When I show our controller using Storcli64, it shows the firmware package as 

FW Package Build = 24.21.0-0139

Hope that heals a bit