I don't think that's optically possible without either a teleprompter or a "punch-hole" display. "Teleprompter" sounds sophisticated but basically a pepper's ghost box for cameras, there are plenty of amateur YouTubers building it "in zero dollars from home waste" manners. Half-silvered glass or polarized filter is nice but not necessary from what I understand.

Somewhat tangentially, what I find from sudden rise in stay-home teleconferencing is that TV hosts as well as corporate teleconferencing users are almost completely clueless about teleconferencing compared to YouTubers and streamers, people think a superwide Logitech webcam and a laptop on your lap in a bathroom is all it takes. YouTubers run Sony Alphas all day with nice primes, some even REDs ARRIs, large dia condenser mics, Shure is entry-midrange there ... So a lot is there to learn from them, especially on budget.

Yes, there's multiple ways of doing it. DIY-Perks has a webcam mod[0] using 2-way mirror.

The other way is using a microLED display. A microLED is so compact/bright that you can leave spaces between elements and can be 50% transparent or more looking from behind. Alternatively Optical/sensor elements could be interspersed with the microLED elements giving as good an image quality as can be achieved based on the area used.

[0] https://www.youtube.com/watch?v=2AecAXinars

The old Microsoft Surface 2, renamed later PixelSense when the Microsoft marketing department decided to launch a new product with the exact same name than an existing product, had a display which was an infrared camera. Each pixel was also an infrared light sensor.