I am trying to update my IOS on my phone. did not work through wifi, plugged into my laptop and just got error 4000 while trying to update through itunes.

Why doesn’t it work through Wi-Fi?

To update over the air from the phone all of these requirements must be met:

• You need at least 6 GB of free storage
• You must be connected to a Wi-Fi network (and not a personal hotspot)
• The phone must be charged to at least 50%, and preferably plugged in so it stays above 50% during the update
• The phone must not be in Low Power Mode
• The phone must not be connected through VPN, and it may be necessary to delete any VPN apps and VPN profiles
• The phone cannot be in Airplane mode
• You cannot still have a beta version installed on the phone

If you can't meet all of them you can still update using your computer.

Error 4000 means there is a problem in your PC’s connection. If you have a firewall or antivirus try turning it off temporarily. Here’s more information about that error→If you see Error 4000 updating your iPhon… - Apple Community

I have this same problem trying to update to iOS 15.4.1 on an iPhone X ,

My battery is fully charged and its plugged in, I've got at least 14Gb space, no VPN's, not in airplane or anything else.

In fact the update downloads just fine, then says there was an error.

This has happened 4 times across two different days now, so this morning I tried to update using my computer through iTunes and got the same error 4000 as the OP.