My T has intentionally left me a few voicemails over the years, including a comforting one I requested after an upsetting world event and once before I went into labor (to sort of have her with me). I have found them both incredibly comforting and not enough at the same. I like having them and hearing her voice and some of what she has said to me on them. But you're right that it's not the same as being together in person and it doesn't always stop me from feeling disconnected or rejected for little to no reason.

I do think it might be worth giving it a try and seeing how it feels. Maybe it will help and maybe it won't. I don't think it's weird or needy, though. Lots and lots of people keep and re-listen to voicemails from people who are important to them.

ETA: She has also left a few messages about scheduling and stuff over the years, and I've kept those too.