I just tried Yliluoma 1&2 on video it right now, and it does about as well as Bayer ordered dithering, since it is a variation on ordered dithering. You can try it yourself, since I built an app[1] that includes the Yliluoma 1&2 dithering algorithms, and supports video.
For anyone that wants to try Yliluoma's dithers for themselves, I have created the only interactive version that I am aware of, as well as the only GPU accelerated version at https://app.dithermark.com
I don't know if it's exactly what you're looking for but I made a free tool https://app.dithermark.com . It only allows 18 colors max, but it has a lot of options, including the ability to determine what color palette to use.
Color dithering is very similar black and white dithering, the difference is that instead of 2 colors (black and white), you have n colors, and you want to find the one that has the shortest distance to the current pixel. There are various formulas[1] to determine which color is closest, and which formula you choose will have an effect on the results. I built a dithering app[2] that lets you choose the distance formula, so you can see for yourself.
Since I see you're using Vue, I created an MIT licensed dithering web app with Vue. I've never tried to embed it in anything, but you're welcome to give it a shot.
It's not a phone app, but I made a web app[1] that can get pretty close[2]. From looking at the images I think the reason why other other apps don't look the same is that they try to emulate it use an ordered dither, while it looks like the Gameboy camera is either adding some randomness or noise as well. I have a Bayer (R) algorithm that adds randomness and it seems to get closer to the Gameboy camera output.
I was thinking about that recently, and I'm not so sure either. The profit margin for Google Services which YouTube is a part of is 30%, but that also contains the ads division, which is hugely profitable. Also, you would expect if YouTube's profit margin was 30% as well they would disclose it, so you have to imagine it must be significantly less.
[1] https://app.dithermark.com