I literally just faced this same dilemma! I went online looking to upgrade the kit lens I’ve had on my Canon EOS 70D for nine years and got sucked into the mirrorless hype.
In the end I sortof ended up upgrading both… I got a great deal on a second hand Canon mirrorless body, and because it has in-body image stabilisation I could then spend a lot less money to get a 25 year old ‘L’ series EF lens rather than a newer one if IS in the lens.
I’m extremely pleased with this set-up so far, and even more pleased that I can add to my lens collection in future for much less money than if I needed IS hardware in every lens.