You can boot TWRP and mess with the system image from there. If you fastboot boot your-recovery-image.img instead of fastboot flash… you should be able to load TWRP once without ever writing something to disk. From there, you may be able to prevent the re-flashing of the original recovery, and then perhaps flash TWRP permanently. You’ll have to look around and figure out what’s possible, but there’s still some hope for you.
If your native OS is maintained longer than Lineage, it may be wise to stick with that. You can also look got alternatives to LineageOS. For example, my device only has partial Lineage support, with community builds on XDA as the only source for ROMs, but crDroid has maintained images available and PixelOS even has an Android 14 ROM I can try.
For your phone, crDroid seems to be released last, almost exactly a year ago, but Asus updated it a month ago. I would stick with Asus’ ROM in this case, and focus on sabotaging the recovery re-flashing.
You could also try to just… build LineageOS and see what happens. Once initial porting is done for an Android version, there’s a good chance very little device specific features will break until the next major version comes out. If you have access to get a Linux server with at least 16GB of RAM and about 50-100GB of free space (Windows may work through WSL but no promises), you can build the entire ROM yourself.