Hi Jan,
I hear great things about the Katana amps. They sound amazing especially for sparkling clean tones. I don’t have a Katana but a good blues tone probably depends on the type of song with respect to how much overdrive you want. In general, a good blues tone is relatively clean with the amp set such that the tone breaks up when you dig into the strings harder. A little reverb and some short (slapback) delay will help fill out the sound.
John

Staying just with what’s accessible directly on the control panel (and not through the computer link), try setting the amp to crunch. Bring the volume up to high, then bring the gain up to the point where you hear it breaking up with a hard attack, but still clean on a light attack. Add some reverb (I prefer the green light), and you might try a little delay, but use the tap tempo to make the delay about as short as you possibly can.

Another thing that’s cool is to do the same thing, but with the Brown channel. You will need much less gain, and will get a thicker clean sound. I tend to test the amount of gain by playing double stops or small three note chords. They break up much quicker than a single string will, so I will set the amp so those are very distorted to my ear (I have a low tolerance for distortion and high gain in general).

Alternatively, you can play with the included Overdrives. Here, I have to completely forego the gain section, or it gets to be too much for my taste.

Here is a little something to match up to:-

JohnStrat

I use a compressor with a reverb + short delay

It means you can have less/no crunch to get more sustain

katana instructional video