Watching portrait footage that’s been padded out to landscape on a portrait device is even worse!
I’m proposing that the web designer writes a responsive webpage when they are sent a portrait video to include, so that if it’s viewed on a portrait device it fills the width, and when it’s viewed on a landscape device it fills the height. If it’s actually for telly, there’s usually no harm in cropping a bit at the top and bottom and at that point, feel free to put whatever you like down the sides, but there’s no need to throw away the portrait original for the portrait view of the website.
Like I already said, the technology for writing a webpage that looks different depending on the orientation of the device being used to view it is neither complicated nor new. There’s no need to treat every medium the same in 2023.