I really like this kind of questions and all answers that appears already here.
So I answer is "it depends" :-).
Are ready to travel over the spiral of learning or you just want to shoot pics?
If you just want to shoot pics, then camera does not matters.
Just have a smartphone, with whatever lens and shoot selfies or other all whatsoever images.
But if you want to learn and continuously improve your skills, then camera really matters, but also in specific way.
As the others already stayed you shall know the camera you want to buy and use it in sense, that you would like to use the features, which it will give you.
There are couple of things I had been experiencing.
Long time ago I was using analogue film point & shot camera. What was the problem with it? I cannot really control depth of field. It was great for landscapes, but almost useless for portraits, as always background was strongly involved in composition. The solution was always to have good background - sometimes very complicated.
Currently I am using mid range DSLR for photography, cell phone for whatever shots and ... the most important ... small wooden frame to train my eyes and brain in composition.
Why or in what way camera matters?
My wooden frame is great tool. I have it with me almost always, even if I am sitting in park, sometimes I am getting this frame and observing surroundings through the frame. I am doing "photos" and storing them in brain memory. Frame helps to see like one see through the camera. This frame teaches me what is a composition, what I like to have in scope of vision. But ... frame has sensor what I have in my eyes - very good sensor in sense of e.g. great number of EV stops, but very different to one I have in DSLR or phone.
When I am finding something interesting, I can take my phone and shoot.
Hmm ... why the image is different than when I was using my wooden frame "camera"?
This question brings us to the second stage.
When composition is nice, interesting and has some topic or might express some idea, the phone limitations might destroy everything.
Too much light without possibility to use manual mode, will end up mostly in overexposed images. Often wide angle lenses in cell phones will end up in high distortions.
For example there is autumn and colours are pastel, at the phone screen I see all oversaturated - especially red colour is very intensive.
So pastel relaxing atmosphere in my phone becomes aggressive mixture of background and topic without possibility to focus longer on anything on the picture.
So the situation I saw through the wooden frame is not the one, which is stored on SD Card on the phone. Or formulating it other way round, there is a big gap between the memory footprint in brain and file on the SD card.
So camera matters.
The same scenery. The same park, the same autumn, the same bank I am having my DSLR.
Switched to RAW manual mode, or e.g. aperture priority. I am decreasing the EV -1.0, I am setting neutral mode for colours. Taking the lens with low aperture like 2,8 and proper focal length. Click. Got a photo ... hmm ... bokeh is giving or enabling possibility to separate topic from background, neutral colours are ending up in pastel colours, focal length makes my picture composed well in sense that topic is well visible. So the photo is similar to what I saw over my wooden frame.
Wooden frame and DSLR are giving more less the same.
So camera does not matters ;-).
Extending question - does tripod matters?
But then I am taking my tripod. The same scene. I am shooting long exposure. No ... OMG ... my wooden frame has no ability to do it. I could only imagine, what will be there, but I do not see it. For example running children are changed into nice coloured bands of lights. Even shape is interesting.
Does filters matters?
I am taking ND 3.0 filter. The time goes so fast. How much movement I can capture. The clouds seemed to stay, but I see they are moving, even on the picture I see where and how they move.
To make the same with my phone, I need to do funny things, and at the end the result is awful.
Does lens matters?
I found small bug resting nearby on the bank. I can use macro/micro lens or extension tubes or magnifying glasses ...
Then we can goes beyond already mentioned. Does lighting matters?
There is a concert and behind the band there are strong lights. Even DSLR might have problems, but fill-in flash or whatever good frontal light will help to get faces or instruments bright enough.
Even further ... does makeup or studio for portrait photography matters?
Finally I want to say. It matters if one might and can use offered features or abilities.
But it does not matter if you will not improve, in between, also your artistic skills like: understanding composition, psychology of the colour, creativity to prepare scene, ability to observe in patience and so on.