What version of macOS was being installed from recovery mode?
Try booting into Internet Recovery Mode using Command + Option + R instead to see if it will allow you to access the macOS 10.15 Catalina installer. Unfortunately some Macs will only boot into the online installer for the version of macOS which originally shipped with the Mac from the factory regardless of the keys used.
For the past two months or so there have been lots of reports here that people are unable to reinstall macOS from recovery mode for older systems and/or macOS (it is unclear if it is system based or OS based). Hopefully if you can access the Catalina online installer.
Otherwise you will need access to another compatible Mac in order to create a bootable macOS USB installer using the instructions in this Apple article:
Create a bootable installer for macOS - Apple Support
Generally you need the following Macs in order to create a USB installer these operating systems:
- macOS 10.11 -- 2007 to 2015
- macOS 10.13 -- Late-2009 to 2017 (mid-2018)
- macOS 10.15 -- 2012 to 2019
You can use the information in the following article to confirm which Macs are compatible with various versions of macOS since what I have listed is just a general guideline....some at the edges of those ranges may not be usable while some outside the range may be compatible. The other host Mac can currently be running any version of macOS 10.6+.
https://eshop.macsales.com/guides/Mac_OS_X_Compatibility
Another option would be to install Linux Mint on the laptop. Linux is a great way of extending the useful life of a computer. It gives you an up to date non-Apple OS which has access to lots of free open source software within the Linux Mint software repository.
FYI, if your laptop uses a hard drive and it did not have Filevault enabled, then you should secure erase the hard drive by writing zeroes to the whole drive so no one can retrieve your data since a simple erase does not destroy data on a hard drive. If the laptop uses an SSD, then you are good to go since a simple erase will cause the SSD to be zeroed. Here is an Apple article with instructions for things to do when preparing a Mac for sale such as disassociating your AppleID/iCloud from the device.
What to do before you sell, give away, trade in, or recycle your Mac - Apple Support