Can I use the scarlet solo paired with the DT 770 250 ohms to listen to recordings at sufficient volume and do things like audio monitoring at good volume levels?
In practise, anything with a dedicated ¼" headphone output is going to be designed to drive 250Ω headphones at comfortable listening levels.
You really only need to compromise to lower impedance if you need extra volume - eg a drummer tracking to a click track - would need 80Ω for that extra punch.
Low impedance headphones are for low output devices such as mobile phones etc.
From beyer's own DT 770 page…
For what it's worth, Focusrite's recommendation is less than 200 ohms for USB-powered interfaces, which includes Scarlet solo. The interface just lacks voltage to drive high impedance headphones at full volume. It's up to you if it's loud enough.