Is "put someone on/over to" for "put someone through/connect someone to" idiomatic?

Question

Where in the English speaking world do they say, "put someone on/over [to]" for "put someone through/connect someone [to]" as in:

If you'd like to speak direct to one of our technicians about anything, feel free to call me at 0088000900 and I'll put you over to them.

(Telec) put me on to Mr. Brown passez-moi M. Brown; (Telec) would you put on Mrs. Smith? je voudrais parler à Mme Smith; passez-moi Mme Smith. (Source: Collins-Robert English-French Dictionary)

PUT ON

To make someone (or something) available for talking to, listening to, or watching via some communication medium or broadcast: Will you put your mother on the phone? (emphasis is mine.)

The American Heritage® Dictionary of Phrasal Verbs

To pass the telephone to someone so they can speak to the person you have been talking to Wait a minute, Mum, I’ll put Joe on.

McMillan Dictionary

Is this usage common and widely accepted?

I looked up put over online, but I could not seem to find an authoritative resource to support that "connect/put someone through to" meaning to it.

PUT OVER

1. Make successful, bring off, as in Do you think we can put over this play? [Early 1900s]

2. Make something or someone be understood or accepted, as in The public relations staff helped put our candidate over to the public. [Early 1900s]

3. put over on. Fool, deceive, as in We can't put anything over on Tom. [Early 1900s]

4. (US) Delay, postpone, as in The meeting was put over until tomorrow. [Early 1500s] Also see put off.

The American Heritage® Dictionary of Idioms by Christine Ammer

Please, consider these sourced examples:

So, I just got off the phone with Plat AMX customer service. I called and told them the offer BoA had given me to move my business. The rep went through all the benefits of the card, and I reminded the agent I had been using them and was familiar. (Yes, I was very friendly and cordial.)

She then said, "Well, let me put you over to Centurion Card Services and see what they might be able to do for you."

A few minutes later, a rep from Centurion was on. She went through the normal security checks and such, then proceeded to thank me for our business and being a good customer, etc. Then came the death nail...."I will notate your interest in the Centurion on your account, and the next time they process invitations, your account will be reviewed." (emphasis is mine.)

FlyerTalk

10:03 a.m. – A call comes in that Mariano answers, this one a 911 call. Two vehicles are involved in an incident. “What are they doing? Let me put you over to Phoenix PD. Don’t hang up, OK?”

Arizona State University

EDIT:

If that usage of "put one on to someone/put one over to someone" actually is acceptable, how do using these phrases in a telephone conversation differ from using "put one through to someone/connect one to someone"?

You might consider the following example:

Mr. Brown - Hello, this is Mr. Brown. May I speak to Dr. Capwell, please?

Receptionist - Surely, Mr. Brown. Just a moment, I'll put you right through to him.

Receptionist - Surely, Mr. Brown. Just a moment, I'll put you right on to him.

Receptionist - Surely, Mr. Brown. Just a moment, I'll put you right over to him.

Answer 1

It's common in English to use that term: example, "Please put mother on the phone." I've never heard this with the word "over," to me it sounds a bit British if you say it that way, but most English speakers would probably understand what is meant by "Please put mother over the phone."

A more fitting statement would be "An announcement came over the broadcast system" or if someone said "I learned about your birthday over the phone."

Like you mentioned before, using 'over' makes more sense when moving something around. Like, "Put this box over there." Similarly, "I'll transfer you over to the fraud department."

Also, "over" can specify the medium of transmission; for example, "over-the-air." But you wouldn't say "I heard that song over the radio," you'd say "I heard that song on the radio," or "I saw that football game on TV"