monterey failed and now not enough hard drive space to do a re-install

Suggest restarting in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time -Normal.

This may or may not allow the upgrade process to complete.

If still not booting up at all - may have to use Transfer files between two Mac computers using target disk mode to transfer the important files off the drive.

In addition, I offer the following. You may have an issue of not enough disk space to do another download because the old upgrade file still resides on your disk and is taking up a lot of space. if so, move it to the Trash and empty it. I have another comment. If the Monterey upgrade failed to install, it was likely corrupted during the download. Did you use Wi-Fi? It's too slow for these very large files and will often fail. Instead, use a wired Ethernet connection for this download and it should go ok.

Get an external drive. Boot to Recovery and install on the external disk the macOS version offered in Recovery. Then boot from that disk and access the internal drive to move files/folders to the external disk to the external drive,. After completing the move download the Monterey Installer and try installing on the internal disk

That would assume the Monterey has flashed the EFI BOOT ROM to the computer first - no.

It is not clear if Monterey is offered in Recovery. It may still be Big Sur.

Worth a try.