Would it really be that much though?

I thought search ads were auctions - i.e. competition for impressions/clicks directly correlates to the price of advertising.

If you have search users distributed across 100 platforms, the competition for impressions/clicks is going to be super low on all platforms, but you'd have to advertise on 100 platforms to get the same level of engagement, adding it all back up but with 100 middle men this time.

Why do you think that? The revenue is determined by the number of searches showing ads, the click-through rate, and the cost per click. The total across all companies would clearly not change for the first two metrics. Would the cost per click change? Given it's determined by an auction, I don't see how it could change. If you have an incentive to bid $1 on an ad on a single site with 100x traffic, you'd be equally willing to bid $1 on each of 100 separate sites with 1x traffic.

And the number of ads and hidden ads would be like Cable.

If there were 100 good search engines for end users, but opinions of different users on quality were highly correlated, the traffic would be very disproportionately on the one that was perceived as even very slightly better.

And they’d make the bulk of the advertising dollars.

And they’d have the bulk of the money to throw at improvements.

And the next year, unless some competitor got more access to outside investment to make up for that, the gap would be bigger, they’d have even more of the search audience, and even more of the advertising money, etc.

a.) close to the point where the money is injected

b.) have quick-adapting prices, ideally ones where competitors bid against each other

c.) are dominated by 1-2 firms with little competition, so they have pricing power.

Google and Facebook tick all the boxes. In COVID money was injected directly to the consumers (thanks to stimulus payments) and to small or mid-size business (PPP loans). Google and Facebook run up-to-the-minute ad auctions, so prices adapt immediately to additional money becoming available. And they have little real competition, so it's not like they can be undercut by competitors.

By contrast, wages (for example) a.) require that your employer have more money, which generally requires that it have trickled down through the whole value chain b.) get updated usually once per year and c.) generally require that your competition also decide they're going to ask for more money too, less your employer just decide to employ someone else. That's why wages are often the last and stickiest place that inflation shows up.

The general phenomena of certain businesses being able to raise prices earlier, faster, and more than others in response to rising money supply is called the Cantillon Effect, and is a pretty fertile ground for making lots of money in an inflationary environment.