Need macOS high sierra installer that is compatible with my macbook air ventura for a bootable usb

You got this bass-ackwards. You need a Mac that can support the High Sierra download and that is not an Apple Silicon Mac, but rather one that supports a direct High Sierra download from the Mac App Store — and that is your 2010 MacBook Pro. That 2010 MacBook Pro does not support Internet Recovery (I don't believe).

You should have posted here first and we could have pointed you to the link to download the full High Sierra 10.13.6 installer, you could have made a bootable USB stick, and then proceeded to wipe the MacBook Pro. Then you would have had a bootable USB stick to perform the reinstallation on that 2010 Mac Book Pro.

Once you find a bootable Mac that supports a High Sierra install, use How to download and install macOS - Apple Support with a Safari browser to get the High Sierra 10.13.6 installer. Then follow the directions in Create a bootable installer for macOS - Apple Support.

Here are the Macs that are supported by macOS High Sierra: macOS High Sierra - Technical Specifications

Try connecting the laptop directly to the router using an Ethernet cable for a faster more reliable connection to bypass hard to troubleshoot WiFi issues. You need a good fast network connection for Internet Recovery Mode.

You can generally use a Mac from Late-2009 to 2018 to download & create a bootable macOS 10.13 USB installer. Or, if you have a Mac from 2007 to 2009, you can instead download & create a bootable macOS 10.11 USB installer so you can then use the "broken" laptop to access the macOS 10.13 installer.

Edit: With a 2010 Mac, that laptop probably shipped with OSX 10.6 Snow Leopard recovery DVDs so use them if you are unable to use Internet Recovery Mode or create a bootable macOS 10.11 or 10.13 USB installer.

What version of macOS is being installed when you boot into recovery mode? I've seen the server issue come up a lot recently, unfortunately users don't provide us with enough information & feedback to figure out what is going on & what may fix it. I do know with the old macOS installers that the installer's certificates have expired which then requires setting the system date to an earlier year (what year depends on how the installer is being access....local recovery or Internet...and which version of macOS). I doubt this is causing the server issue, but it is hard to say.

If you actually have a 2010 Mac, then you should also have the original OS X recovery DVD which shipped with the computer from the factory which can be used to reinstall OS X 10.6 which will then allow you to at the very least install macOS 10.11 which can be downloaded using your 2020 Mac since that download is available outside of the App Store (you will need to transfer the downloaded .dmg file to the 2010 Mac to be used though).

Please confirm the exact model by entering the system serial number here:

Check Your Service and Support Coverage - Apple Support

It also happened to me on a late 2011 MacBook Pro. The progress was kind of hard cause I had no access to another macbook (idk if this is legal to recommend) but I used this thing named "vm ware virtual machine" downloaded the MacOs 11 iso (would recommend watching a tutorial on youtube and be careful with which video you choose cause some people make you download viruses, etc) and did all the progress to install it through the App Store and it worked just like a real macbook! Right now I am on the MacBook Pro thanks to the virtual machine and the bootable device.

Sierra is available in .DMG form. So you could use the new Mac to download the .DMG file and put it onto a USB flash drive or HFS+ formatted external drive. (Just as a file, not as a bootable installer.)

That would still leave the problem of booting the old Mac up so.that it could mount the .DMG and run the installer.