It depends how close you sit to your TV and how large the TV is. I can tell a difference if I'm close enough or if the screen is large enough. As well, try turning on a streamed 1080p show and using a 4k bluray (if you have all of thrsr things). When you stand close (like, closer than you'd watch), you can really see the difference. As you back away, it becomes less noticeable, but even at comfortable viewing distances people can see the difference

You can see an example on your phone. Try watching a video in 1080p and then 480p. You should notice a difference, even if you hold your phone a foot from your face it's the same idea when watching on a tv.

HDR vs no HDR makes a big difference in colours to me. And if you compare compressed low Bitrate footage vs higher Bitrate there will often be artifacts or color banding, particularly in darker scenes or wherever you have gradients.

It ofc also depends on what device you are watching it on. But I would say that yes if you have a movie (made up example) that is compressed to 5gb total size vs 25gb vs 70gb for the uncompressed Blu-ray quality, then the first jump will be a very noticeable difference assuming you have capable hardware. Whereas the second one will be much much less noticeable and also come with other drawbacks that need to weighted off, e.g. storage requirements.

For a game you can tell. For a movie, it's honestly pretty hard. The biggest difference with most 4K media is the HDR which I do appreciate a lot more than extra pixels.

Open up this webpage on your TV (or whatever display you use to consume media) and watch the moving line. If you can notice aliasing at your normal seating distance (I.e. the "jaggies"), then you would benefit from a higher resolution display. Otherwise I wouldn't worry about it.