Word/phrase for over asking as a tactic to get what you really want

I'd call it overshooting:

to go further or do more than necessary or expected
_{Cambridge Dictionary}

For example:

How high should I overshoot the salary question during the interview process?

Anchoring high

If websites on negotiation are to be believed that kid has professional negotiating instincts.

Anchor first and anchor high and you'll be playing in the big leagues is an article on the psychology of negotiation. The anchor is the first sum on the table and the article, unsurprisingly, suggests the negotiating party ask for a higher sum than they would be prepared to take. Harvard Law School gives some advice on how to overcome the anchoring bias.

I don't see how it is fundamentally any different, as a tactic, from bargaining.

In the latter the seller starts off by asking a higher price than that for which he/she would be prepared to settle, and the buyer begins by offering a lower price than they would be prepared to pay.

So a child, negotiating with its parents simply begins by asking for more than they really want, and the parents may start by offering less than they are prepared to give.

Eventually a bargain may be struck

You are talking about the “Door in the face” method.

https://en.m.wikipedia.org/wiki/Door-in-the-face_technique