My thoughts exactly when reading this.
I believe people when they claim to develop free software. Often because it's software the dev wants for themselves anyway and they've merely elected to share it rather than sell it. The only major cost is time to develop, which is "paid" for by the creation of the product itself.
You (OP) are proposing a service. Services have ongoing fees to run and maintain, and the value they create goes to your users, not you. These are by definition cost centers. You will need a stable source of funding to run this. That does not in any way mix with "free". Not unless you're some gajillionaire who pivoted to philanthropy after a life of robber baroning, or you're relying on a fickle stream of donations and grants.
You indicate in other comments you will not open the source of your backend because you don't want it scooped from you and stealing your future revenue. That's fine, but what revenue? I thought this was free? What's your business model?
It sounds like what you want to do here is have a free tier anyone can use, supported by a paid tier that offers extended features. That's fine, I guess. But if you want to "compete with DuckDuckGo", you are going to need to generate enough revenue to support the volume of freeloaders that DDG does. If your paid tier base doesn't cover the bill, you will need to start finding new and exciting ways to passively monetize those non-revenue-generating users. That usually means one or more of taking features away and putting them behind the paywall to drive more subscriptions, increasingly invasive ads on the platform, or data-harvesting dark patterns.
Essentially what I'm saying here is, as-proposed, the eventual failure and/or enshittification of your service seems inevitable. Which makes it no better than DDG long term.
It is, at any rate, a very intriguing project.
It's a factor of 8 we're talking about. That's not far off from a factor of 10. If a factor of 10 difference is important enough to get its own prefix in SI, I think a factor of 8 difference is plenty enough to care about having clarified notation. This isn't like the mega/mebi thing where the drift is only on the order of 3%.