Long ago in a galaxy far far away, I worked on (audio) three cam live switched legal edu seminars. As I recall, my video associates, used a device called a 'moderator', which had a VGA pass-though to feed the projector and converted it to composite or component video to feed the switcher.
There is probably an easier, less costly way now. Now-a-days, I get the Power Point (or Keynote) file from the presenter.
Maybe OBS can be run concurrently if you have access to the source PC. and can install it in
Otherwise, you could point a locked-off cam at the screen.

Moyea PPT video converter.  http://www.moyeasoft.com  I used this a few years ago with success but it does cost a little.

Take a look at https://www.vegascreativesoftware.info/us/forum/presto-from-singular-software-for-vegas-in-beta--78250/#ca452945 in the Archives. This came up about 8 years ago but perhaps the thread will give you some ideas.

Frankly, I would purchase PowerPoint and use its excellent feature to produce mp4 video, or png/jpg files. Slides shot from on-screen tend to look soft and have strange color deficiencies.

Thanks all for your suggestions.

@JackW So, does Powerpoint can do the same as Moyea do ? And does the conversion from picture (with text) to mp4 file is done without too much loss of quality ?

It outputs as 1080p (1920x1080,) 720p and 480 video. It does not export jpg files, however. Text in Powerpoint is always a problem when coming into video because of font styles and sizes. Fonts with serifs often break up and small sizes are often unreadable.

"Text in Powerpoint is always a problem when coming into video because of font styles and sizes"

Yes, but if you just need a static shot of the PP slide, a screen shot (or part of) maintains the text and picture quality nicely. I've been using 'Lightshot' for an art history landscape painting lecture series. LS allows cropping, copy, save, ect. I save the images as PNGs.