All you really need is a little plastic thing of needles ($1), some pins ($1), thread (varies but even good cotton thread isn’t that much), scissors (where you might actually consider investing a little - do not use these scissors for anything else, and consider a rotary cutter if you really get into it), and fabric.
Fabric might seem like the pricey part of the equation, but consider how much a thrift store is going to charge you for a duvet or a pile of t-shirts! I have something like 30 t-shirts I spent maybe $5 on several months ago, and I’ve been working through that pile for a while.
You can turn a t-shirt into a pillow, a reusable bag, use the scraps to patch clothing, make dolls, quilts… The bits that get to be so small to be unusable for a scrap quilt you can use to stuff things.
It takes a lot of time compared to machine sewing, but it’s an activity that can be done while watching a tv show.
I often do the opposite, pick a bright color that is not the color of the base material, to make the repair stand out more.
I do that too! But it depends on the repair. If I just fix a seam or a tiny hole in a shirt (you know, the ones that you need 2 stitches for) then it won’t stand out and look cool but just look out of place to me.
But I agree, in general visible mending is nicer and easier.