To make it short, I have some familiarity with Krita but I am not savvy enough to figure out how to alter the brushes, to make their bleeds more transparent and let it blend better. My current version is 4.2.9..
Is there any way to change this?

It depends which brush you're using. Which brush are you using there?
In your picture, the change of colour at the edges isn't something I get when painting with Basic-2 Opacity above or directly on a black background layer.

For the Auto tipped brushes, you can select a mask type of 'Soft' and adjust the Softness curve, if that helps: https://i.imgur.com/OOYFYnE.png

In the sample I used the draw brush from David Revoy's brush kit, however, this problem is present in all default and kit's brushes. Say for the pixel (obvious reasons) and certain blending tools.
And unfortunately, the softness curve doesn't seem to fix it.

What is the color space of your document? (See the bottom bar of Krita). It looks like an issue with the blending math which is often a result of either weird blending mode of the layer or canvas or the brush, or weird color space.

....Oh.
Ok, yeah, looks like I forgot to switch out the color space, since I needed a specific type for an assignment (CMYK). In that case, is there a way to switch that in the existing document?

Image -> Convert Image Color Space.

Also, next time you need to have a CMYK project, it's really recommended to work in RGB first anyway. You can always convert, you can always see the proper colors using the soft-proofing, and the CMYK profile that Krita ships by default is only valid for some cases; for most, you should ask your printer for a very specific profile that they use.

Alright. Thank you for the help and advice!