This article explains how to get apps that aren't in the App Store by sideloading apps from developers or jailbreaking your iOS device.
How to Install Apps Without Apple ID Password / Download App from App Store Without Password iOS 17
Perhaps the easiest way to add apps to your iPhone without using the App Store is by using a technique called sideloading. Sideloading is the name given to installing apps directly onto your iPhone instead of using the App Store. It’s not a common way to do things, but it can be done.
The real problem with sideloading is that you need the app in the first place. Most iPhone apps are only available in the App Store, not for direct download from the developer's website or any other source.
But some developers make their apps available as direct downloads to get around Apple’s rules. If you can find the app you want to use, just add it to your iPhone (the developer will likely provide instructions) and you should be good to go.