SE doesn't recognise the internal HDD

You will have to use the floppy startup discs to boot the machines in order to run the Disk Repair Tool, partition, and format the HDD if it is still functional. Only then can you install MacOS onto the HDD. That's about all that I remember.

Launch/Utilities/Terminal and copy & paste this command at the prompt:

diskutil list

Press return.

If it sees the disk, note the number of the disk (far left column) you want to mount.

Then, enter this command:

mount /dev/(number of disk)

Put in the number no parenthesis.

Press Return.

Also might try

mount force /dev/(number of disk)

Doesn't matter. It is for OS X, Unix hasn't changed in 30 years

The Apple HD SC Setup application on Disk Tools (or system) floppies was intended for original Apple SCSI hard drives. If the hard drive had been reformatted with a third-party utility (or if the internal hard drive is not an Apple one), an appropriate third-party formatting utility would normally be needed. For example, Lido 7.5.6. The problem is that a plain Macintosh SE (not FDHD) has a floppy drive for 800K (not 1.4 MB), which means that there is relatively little space for floppy disk modifications.

Which operating system do you have on your system floppy disk(s)? Exactly which disk utilities have you tested? Is there an Apple logo on each hard drive?

Is the SE/30 that you mentioned fully working? Which operating system is it running? Do you have access to System 6 or 7 floppy disks?

If necessary, the SE/30 could be used for the handling of downloaded files and for floppy modifications.

In addition to the Disk Repair tool if you have access to SCSI Probe, which was a common utility/control panel, it will show you all the SCSI disks attached to the Mac. It will show a list of SCSI devices, including the Mac itself. When you check you'd expect to see two entries. One for the Macintosh SE and one for its hard drive.

If you don't see the hard drive try connecting an external SCSI device like another hard drive or CD ROM drive if you have any to rule out any issues there.

If you are comfortable opening the case then you can try unplugging the SCSI cable from the drive and the logic board and attach them again. You can also swap disks from a known working drive to see if works in the troublesome SE and the troublesome HD in a Mac that you knows recognizes HDs fine. If you have an external SCSI HD enclosure you can also try putting the drive in that. Doing all of these will help narrow down where the problem is.

It may be a ROM or SCSI controller issue, but usually when either those are the issue then there are also other problems with the machine, like the zebra-like vertical lines (which my SE FD's suffering from at the moment due to a leg in its high-ROM is broken).

Usually in my experience the HDD is either disconnected (cable loose) or needs to be reformatted for whatever reason. Hopefully it's one of those.

A word of warning though, If you do open your SE(s) be careful not to touch the exposed CRT (monitor) or power supply (this should be enclosed). Doing so can potentially give you a nasty shock. If you're worried then wait a few hours after disconnecting the mac or discharge the monitor manually. The harm that these CRTs are a bit overblown, but it's still best to play it safe and avoid touching it (unless your discharging it).