Why the call wins the job
In chat you are one of four. On a call you are the only one, and the customer can hear that you have done this before — which is exactly what they cannot tell from four similar-looking messages.
A call also ends the comparison. Scheduling, access, the detail that changes the price: five minutes of talking settles what would take two days of messages, and during those two days the other three are still typing.
Ask after you have been useful, not before
A first message that opens with "what is your number?" reads as a sales funnel and gets ignored. The same question, after you have given a range and shown you understood the job, reads as the obvious next step.
The order matters more than the wording: answer, show you understood, then ask. Asking first is what makes it feel like a call centre; asking after is what makes it feel like someone getting on with it.
Give a reason and a time
"What is the best number to reach you?" is weaker than "I can go through access and scheduling in two minutes on the phone — what is the best number, and when suits you?". The second names what they get and bounds what it costs them.
If they do not give it, nothing is lost: keep answering in the chat. A customer who prefers messages is not a customer who is refusing you.