How to turn my iPad into a projector?

Then you absolutely need a projector. The iPad cannot project an image on a wall. Not sure why you even thought this was remotely possible. Projectors use a combination of lenses and lamps to project the image. Things the iPad lacks entirely.

Plug a Lightning Digital AV Adapter or Lightning to VGA Adapter into the charging port on iPad. Connect an HDMI or VGA cable to the adapter. Connect the other end of the HDMI or VGA cable to the display, TV, or projector. If necessary, switch to the correct video source on the display, TV, or projector.

I searched this up.

I realize you said you don't want to buy a projector. But, in case you change your mind, there are some available on Amazon for less than $50. They are probably not the best available but in you only need to do this occasionally, they might be useful.

You can use Airplay to stream the content to a television. I realize it's not quite what you're asking.

Use AirPlay to stream video or mirror the screen of your iPhone or iPad - Apple Support

No. Short of Magic, there is no way to turn an iPad into a projector. It has a screen, and shows things on the screen.

AhsokaTano22 wrote:

Plug a Lightning Digital AV Adapter or Lightning to VGA Adapter into the charging port on iPad. Connect an HDMI or VGA cable to the adapter. Connect the other end of the HDMI or VGA cable to the display, TV, or projector. If necessary, switch to the correct video source on the display, TV, or projector.

I searched this up.

They don’t have or want to buy a projector, and don’t have a TV. So, that’s not really going to work. Despite being the only reasonable solution.