With auto iso set the max iso higher to 12800 as the X-T3 can handle high iso well. Perhaps open the aperture at the widest and focus on the cat's eyes.
We all have scenarios, to shoot stills @ 1/20 with ~35mm. I would drop my shoulders, go gentle on the shutter release button at the top or bottom of my breath, and keep elbows closer to my body. If I can brace myself against a wall then it helps greatly. Shooting at low speed takes practice no matter what camera or lens. Once you understand the basic relationship between shutter speed, aperture and iso, with good camera holding technique you'd be so far ahead. However I don't shoot below 1/125 with my cat even if she is "still". At 1/60 I'm really pushing my luck, even if she is sleeping. BTW you have such cute cat!