I have a telephone video recording I would like to edit to make it appear it was taken from further away than it was?
When you shoot from further away you use a "longer" lens, in other words a lens with a longer focal length. This has a few effects, that you'll have to fake to make it look real.
First, the perspective tends to get flattened with long lenses. You've probably seen this in the classic cinema trope of a long shot of a crowd walking along a footpath, where everyone seems to be about to step on the heels of the person in front. This is because the angle of view is very shallow, so someone in the foreground is not going to be much bigger than someone in the background. Conversely a wide angle shot has exaggerated perspective. See just about any Public Enemy video where Chuck D and Flavour Flav pop their heads into the camera and get massively bigger than the people in the background, just by moving a few feet.
This perspective compression is going to be very difficult to fake after the fact, unless you're really good at rotoscoping and compositing.
If you look at the long lens shot you'll also see that there's often a pretty shallow depth of field. This is often used by film makers, like Scorsese in this clip from Taxi Driver to highlight the central character, by racking the focus to follow them.
Now a wide angle lens and a phone lens (for different reasons) have very deep depth of field. So you'll have to selectively blur the foreground and background. However if you do this without matching the geometry of a telephoto lens (the compressed perspective discussed earlier) it's going to look like it's actually teeny-tiny, because it will look like another kind of lens with a shallow depth of field, a macro lens.
Another thing that telephoto lenses do is magnify any camera movement, where small movements are magnified by the narrow field of view. You could fake this by reframing, using a wiggle expression to drive the movement, however it might not necessarily achieve the look you want: If you're shooting telephoto you're unlikely to hand-hold the camera because it would look awful, so you'd lock it down on a tripod - see the shutterstock and Scorsese examples.
So depending on what the subject of your video is, this could be quite a challenge. Of course if your phone has a 4K sensor, you could actually make a telephoto shot out of a wide by just cropping. Of course this reduces your resolution, so it will look pretty ugly on most phones, and obviously you have to compose the shot with all the action in the center.
Practically you can't do this. The best you can probably do is make it more shaky and grainy. You could also drop the resolution to make it look like it had been digitally zoomed in.
The reason you can't practically do it is because of perspective. When you shoot video from close up, the angle of view is much closer. A small difference in distance to the camera results in a much larger change in size. People's noses look bigger, their ears look further back, cheeks look puffier and shadows fall differently because you see different angles of the person's face than you would see from further away. You can't really fake this, you can try by photoshoping every frame extensively, but this would be massively time consuming and the result would still be substantially lower quality than actually using a long lens to shoot from a distance.
The reason the alternative suggestions work is that they bring to mind other triggers people have for language in video that suggests something was taken from far away. Adding noise or dropping resolution additionally makes it harder to see the perspective issues that say it was shot from up close. Shaking makes it feel like it was a long lens since smaller movements are noticeable when shooting from further away. Noise and drop in resolution are typical of digital zooms, which people are also used to seeing. It won't fool someone who knows what they are looking for, but it will communicate it as a plot device pretty clearly still.