If another airplane is flying an approach into the airport, you cannot
depart IFR. In those cases ATC may assign a VFR departure. You see an avoid
the other airplane until you reach your cruising altitude.

Oh, my.

It's not up to me to decide whether I can depart IFR because "another airplane
is flying an approach into the airport". I either get a clearance, or I don't.

AFAIK ATC can't "assign a VFR departure". Please show me where it says they can
do that.

*I* can decide to depart VFR rather than wait for a clearance. That is not an
IFR operation. In that case I am VFR, until I obtain a clearance, whether that's
at my cruising altitude or some other altitude.

*I* can request a VFR climb while on an instrument clearance. "VFR climb" is
defined terminology. "VFR departure" is not.

Others say a VFR climb can be requested right from the airport surface, with the
issuance of an instrument clearance for departure. I've never seen/heard this
done, but I don't see any regulatory reason why it should not be possible, and I
defer to those who say they have done it.

Dave