As far as I know, open file formats have become the standard for basically all industries and types of files. However, some of them, like the Microsoft Office Formats, are still proprietary. I have seen Open Office documents and Ogg being recommended for Office documents and audio files, respectively, but I'm somewhat confused about other types of formats like video.
Video is tougher as it changes every few years. Once a new standard is out there is also a little lag before there is hardware decoding. Additionally the video codec and extension are different things. I’m going to talk about codecs as I think it’s more important than file type.
Hardware decoding is important especially for mobile devices and software decoding will run the processor and eat up your battery.
For video, right now, the technically best format I think is AV1. If I’m not mistaken it’s open source or at least doesn’t have royalties.
Images are kind of the same story, but browser support is the issue.
I think jpegxl is supported to be pretty great, but Google is trying to push their own standard which I believe is technically inferior in some ways. Because of that Google had support for jpegxl in chrome and then they removed it from chrome.