Issue while reinstalling OS using internet recovery

That error may also be due to the installer having an expired certificate. In that case you would need to set the system date to 2020. But the easiest method would be to attempt to access the online macOS 13.x Ventura installer using Command + Option + R as suggested by @BDAqua. Unfortunately no matter which keys are used to access Internet Recovery Mode, some Macs will only boot to the oldest online installer.

If that is the case changing the system date is the next option to trick the installer. From recovery mode launch the Terminal app from the Utilities menu on the menu bar. Use the following command to set the system date & time to Jan. 2, 2020 @ 11:33am:

date  -u  010211332020

Assuming there are no errors, quit the Terminal app and select the "Reinstall macOS" option.

Make sure to correct the date & time once macOS has been reinstalled.

Like many others, I ran into the dreaded “The recovery server could not be contacted” message when trying to do a restore of Mac OS High Sierra for a 2010 13 inch MBP that I was selling (yes I know it’s worth almost nothing, but someone wanted to buy it from me)…

MacOS High Sierra Problem - Apple Community

1. Start up from macOS Recovery

Option-⌘-R

Upgrade to the latest macOS compatible with your Mac.

APFS won't work for Sierra, Sierra needs MacOS Extended Journaled. High Sierra won't work fir APFS on earlier Macs.

What has often worked for others is to use this Restore Method instead of CMD+r keys...

Option-⌘-R

Upgrade to the latest macOS compatible with your Mac.

2017 iMac failing to install Sierra in re… - Apple Community

Clean Install of High Sierra: Multiple Fa… - Apple Community