Note - I've always given my number first (and all consultants tend to) and it's worked out fine.
Note, most people don't like dealing with places that are not upfront with the number to purchase the item / time etc. So if you are selling your labor, have some sense of its value /price.
The concept of your "worth" as the salary that you can manage to negotiate is so stupidly backwards that I cannot express how much it makes me want to burn everything to the ground.
There is no objective measure and you likely underestimate what you are "worth" to some companies.
As a consultant it might be different because roles are different and you aren't really talking to HR at that point, e.g salary negotiation
Usually that comes with the offer letter, or comes with the numbers that the recruiter reads to you before the offer letter.
But this is usually much before offer letter.
"I've actually done a few of these calls at this point and i know what the best practice / right move / way to play this is, so instead of me telling you what i'm looking for i'd like you to tell me the range on your hiring document:)" and just be totally silent.
Worked twice for me now.
Most people want to fill the audio void and will talk. Extensively.
Now I ask back with “what is the total compensation for this position/role?”. I almost always get an answer, often above my expectations. I used to give my range (mistake)
When they answer "no, we want you to give a number first", I'm at loss about what to do, so I usually give them a number. Answering "no, you" feels kinda puerile.
I assume you have to be the first to do the power play?
Do your homework. These days it's not that hard to determine what a competitive rate for a job is. Then ask for the top end of that, or even a bit more. It shows that you know what you are getting into, what you are worth, and quickly surfaces that there's been a misunderstanding about the job, if there has been one.
Sure maybe push back a little to see if they'll throw out the first number. But don't dance around it too much. Have your number in mind.