NOTATIO

The question is should I use a rectangular frame for instrument name changes (for example to note when a clarinetist changes to a bass clarinet, or flute changes to piccolo)?

if so, should it be
(unboxed) "to piccolo" ________________________ (boxed) "[piccolo]"
or
(boxed) "[to piccolo]" _____________________________ (unboxed) "piccolo"

or should both be boxed?

I know it's a rather nit-picky question.

The reason I ask is that if I box the "to" instrument change, then when the new instrument arrives it can rely solely on the instrument name appearing at the head of that system/line.

If I box the arrival of the new instrument, then I redundantly have both the instrument name at the head of that staff, AND as a text item just before the first notes of the new instrument.

My system: at the change bold and underlined below the staff - FL. 2 muta in PICCOLO. At the entrance of new instrument bold boxed above the staff - PICCOLO.

I have the "to piccolo" in bold font, and "piccolo" in bold font and boxed.

I prefer change announcement "prendre Flute alto" in regular (but bold is also fine if this is your house style), then boxed when the actual entrance takes place. As you did.