What mac OS version are you using?
Does the issue occur if you boot in safe mode? (I’m not actually sure deepdwn will launch in safe mode, but would be good to know)
Have you noticed any similar issues in other applications?
I'm using Ventura 13.4.1 I booted into safe mode. Deepdwn launched and worked as usual in safe mode. And the same spellchecker issue happened. I haven't noticed any issues with other applications.