New lens & camera body or lens only?

Aug 8, 2020

I'm relatively novice in understanding camera hardware and so apologies if this is a dumb question.

I currently have a Sony A7 (the original) with its stock lens; a Sony FE 28-70mm f/3.5-5.6.

I use it primarily for video (recording piano covers for YouTube). I've noticed however that it's not particularly sharp. In this video of mine for instance, you'll notice that the landscape scenes in particular are fairly blurred and lacking in sharp detail:

Also, there tends to be a lot of grain/noise and even more blur as soon as you go into low light, as you can see in this other video I did, which is clearly quite appalling in video quality:

So, I'm firstly considering getting a new lens. Specifically, I'm looking at the Sigma 16mm f1.4 lens, which would be a nice contrast to my current lens as it's much wider and has a lower f stop which would be better for low light. I know this would obviously be an improvement over my Sony lens as far as the amount light in my image, but my question is whether it would also solve my blur and noise issues? Could upgrading a lens alone really make my video THAT much sharper?

My other option if this isn't the case would be to buy a Blackmagic Pocket 4K ( which I have rented before and loved) AS WELL AS the Sigma 16mm f1.4 (the MFT variant obviously).

For reference, I'd love if my videos could reach near the same level of clarity as this video:
View:;dr...would buying the Sigma 16mm lens ALONE for my current Sony A7 camera do this (and significantly reduce the noise and blur that I'm currently getting) or would I also need to invest in a better body (the BM4K's the one I'm looking at)?