How to map a pole erected specifically for a birdsnest

In general it is not a good idea to map bird nesting sites per se: they are changeable, some are protected by law, and mapping sites may, at the very least, do nothing for OSM's reputation with conservation organisations.

Mapping highly visible man-made objects, which are intended to enable birds (or other animals) to nest is different. I would therefore agree with Andy Mackey that something in the man_made category is best. My suggestion is that for the general tag be man_made=artificial_nest, but that if the nest is attached to another man_made object, such as a chimney or tower then artifical_nest=yes can be used.

In the classic case of storks nest this would then be man_made=pole, artificial_nest=yes. Obviously this can be extended to, for instance power=tower, artificial_nest=yes, and other categories of objects (chimneys, church towers, telegraph poles etc). The general tag could also be used for other types of artificial nests: bat boxes, bird boxes, artificial sand banks (for hirundines), tern rafts etc. The type of artificial nesting aid could also be added (note that these are typically known by a given target species: tern rafts are used by terns, but also by gulls), barn owl boxes may be used by other raptors.