I can't think of anywhere else on the web to ask this, so please excuse the basic, out-of-place question.

My wife is thinking of doing telehealth psychotherapy. To create a good therapeutic environment with the client, it would be good to have clear sound, without a mic in her face. Unfortunately we live somewhere with lots of chirping birds, barking dogs and cicadas.

I'm thinking that a lav mic can be hidden near her face, but might pick up too much ambient noise. A shotgun mic (just out of frame) might isolate the audio, but people say that they get phase problems when used inside.

What type of mic would be the best choice for video calls in an environment with background noise? I'll do whatever post-processing the computer will allow between the input and video application. Currently looking at a SE Electronics Promic Laser, which is a budget shotgun. I've got a behringer audio interface with phantom power.

I'm not necessarily looking for specific models, but just the type of mic

Indeed, shotgun mics don’t like reverberant spaces, but with lower volumes and a distance to the mouth of around a foot it will make a voice sound better. But it won’t filter out strong background noises.
I assume your wife needs a live solution? Then take a look at a live denoising app like Krisp, which can be used with the well known conferencing apps.
Krisp is subscription based, this Reddit thread mentions a couple of free alternatives: https://www.reddit.com/r/OnlineESLTe...e_suppression/

https://krisp.ai/pricing/

It's not like you are shooting a movie and need the microphone out of sight.
Use a small unobtrusive headset/earset style mic like a Countryman and get the mic near her mouth.
It will not be that noticeable, and will improve the sound quality over a shotgun style microphone used from a distance.