Here I will guide you to Install the HPE Service Pack for ProLiant (SPP) using Compute Ops Management (COM) on VMware ESX Server.
(Will work similarly with Windows Server also.)

There is a new Note in the Manual:
Compute Ops Management updates the iSUT mode from the default AutoStage mode to AutoDeploy mode after iSUT is installed or upgraded to version 2.9.3 or later. If a reboot is required during a firmware update, it will proceed regardless of the iSUT configuration.

Therefore, the following ESX settings are now only necessary for older versions:

Start the ESX Shell and SSH on the ESX Server:

Optional: Set ESX into Maintenance Mode

Activate the HPE Software Update Tool (SUT):
sut -set mode=AutoDeployReboot
To Check:
sut -status

To check above 2.9.3:

Set the iSUT enableiloqueuedupdates flag to true.
Use the following iSUT command to set this flag:
sut –set enableiloqueuedupdates=true

If you installed or updated the iSUT version or changed the mode, reset iLO or the server, and then wait for five minutes before initiating a firmware update through Compute Ops Management.

You only need to set this the first time for each server.

Go to https://common.cloud.hpe.com/ and start COM:

Now, it’s simple.
Select the Server, you want to Update and Actions > Update Firmware:
(It is currently a bit misleading, because this can also be used to update the drivers.)

Select your Setings:

In this case, the update will not be performed because we have also selected the drivers update, but for this the ESX server must be in maintenance mode.

Problem solved, now it works:

COM checks which firmware and possibly drivers are required and only these are transferred to the iLO board. This is different from before.

At one Point Firmware of the iLO itself is being Updated, and then iLO is offline for some minutes.

Attention: Do not click here! Lay back and Drink your ☕.

Now iSUT inside ESX (or Windows) should pick up the Driver:

Attention: Can be a long time until the Update starts, the default is 5 Min., don’t be nervous!

If you like, watch the Progress also here in iLO:

When everything is done, the Queue will be empty, and the Server reboots (If in Maintenance Mode).

During the Reboot, some post Firmware updates will be done (UEFI, PICs).

Complete!