I can not find any HDMI to DisplayPort cable that support 120hz and 3440x1440p.
Not a cable or converter...
Well, not sure how the new consoles will handle ultrawide resolutions, but with the HDMI 2.1 standard still being somewhat rare on video cards/tv/AVR it's not a suprise that cables aren't readily available. I did find adapters though, which work just fine, but no mention of 21:9 resolution.
If it were me, I'd grab a small-ish OLED that supports HDMI 2.1 and variable refresh and call it a day. If you're stuck on LCD you could do the same, but I'm not aware of any that support variable refresh (those features are usually reserved for the higher end models that tend to also be large).
What all do you plan to hook up with this display?