Posting this as a solution write-up, because I was completely stuck for days and this finally worked.

Machine:

• iMac 27" 2017 (iMac18,3)

Problem summary:
After a wrong macOS installer (created on a MacBook and used on an iMac) + OpenCore Legacy Patcher, my system entered a state where:

• Ventura / Sequoia installers always failed (“Installer is damaged”)
• Catalina failed with Apple server communication errors
• Internet Recovery was unreliable or broken - not working at all for any MacOS
• USB installers didn’t work
• Full disk wipes, APFS/HFS+, First Aid, NVRAM/SMC resets didn’t help
• Hardware was confirmed working before this

The MOST IMPORTANT part (do NOT skip this)

You must first install an OLD, Apple-signed macOS (for example macOS Sierra) downloaded directly from Apple.

This part can be done from Windows.

Step 1 – Install an old macOS (Sierra) using Windows

1. On a Windows PC, download macOS Sierra DMG from Apple
2. Create a proper bootable USB installer for Sierra by following these instructions: 👉 (https://apple.stackexchange.com/questions/448120/how-can-i-use-windows-to-create-an-os-x-el-capitan-or-macos-sierra-usb-flash-dri/448121#448121 – follow it exactly and use every program that is used here, very important (for example do not use winrar instead of 7zip)
3. Boot the iMac from this USB
4. Disk Utility → Show All Devices → erase the physical disk
   • GUID Partition Map
   • HFS+ (Journaled)
5. Install macOS Sierra (no OpenCore, no patches)

Once Sierra boots successfully, the system is finally back in a kinda “trusted” state.

What you need next (hardware)

You will need 3 things (actually 6):

1. A second Mac (MacBook in my case)
2. Two external drives
   • 1× USB (for installer)
   • 1× external SSD (target install disk)
3. If using a MacBook:
   • Wired external keyboard
   • Wired external mouse
   • A USB hub / adapter (to connect everything)

⚠️ Important: during some boot stages, MacBook built-in keyboard & trackpad will NOT work.

Step 2 – Create the correct OpenCore installer (VERY IMPORTANT)

On the MacBook:

1. Download OpenCore Legacy Patcher
2. Open Settings
3. At the top, change the target Mac model
   • Example: iMac18,3 (27" 2017 5K)
   • ⚠️ Do NOT skip this – wrong model = broken install
4. Download the desired macOS
   • (In my case: macOS Sequoia)
5. Create the installer on the USB drive

Step 3 – Install macOS on the external SSD

1. Shut down
2. Power on while holding Option
3. Plug in:
   • External keyboard (wired)
   • External mouse (wired)
   • USB installer
   • External SSD
4. Choose Install macOS Sequoia
5. (If needed) Disk Utility → erase external SSD
   • APFS
   • GUID
6. Install macOS to the external SSD

Let the installation fully complete and boot to the Sequoia desktop.

⚠️ CRITICAL WARNING:
Once Sequoia boots:

• Shut down immediately
• DO NOT run OCLP
• DO NOT install patches
• DO NOT touch anything

This is very important.

Step 4 – Final OpenCore installation (this makes it bootable)

1. Power off
2. Disconnect the external SSD
3. Boot back into the old macOS (Sierra / High Sierra) on the iMac
4. Download OpenCore Legacy Patcher
5. Connect the external SSD
6. In OCLP:
   • Install OpenCore to the external SSD (make sure it says Host device in OCLP settings)
7. Shut down
8. Power on → hold Option
9. Select the new macOS (Sequoia)

macOS should now boot normally.

If required, install Root Patches via OCLP after first boot.

Final notes

• If you try to boot the new macOS before installing OpenCore from the old system, it will error out
• The old Apple-signed macOS install (Sierra / High Sierra) is the key that fixes the broken installer / trust state
• This looks like a recovery / installer trust chain issue, not hardware

Hopefully this helps someone avoid days of frustration.
This method was the only thing that worked for me.