I have ILR and just flew from London to Ohio on Monday, which was the day this new form took effect. I've been going through some personal/family issues recently which was the reason for travel, and I'm staying here until summer.
I printed out the form but they never asked to see it. One of the check in agents asked me why I was traveling, I told him. Then I pulled out my US passport, he saw it, and was like "Oh, that's alright then." And that was the end of it. I was honestly expecting to be questioned more, but it was quick. You definitely need proof of a negative Covid test though. I was asked for that several times. That seemed to be much more pressing than the "reason for travel."
I know I had no issues, but if you're leery about traveling now and aren't in a rush, you could wait until May when things are officially lifted. I don't know about the "other" category, but I do know that lots of airlines are allowing passengers to change their flight dates at no extra cost. So, there's that in case you weren't permitted to travel for whatever reason.