The Google app, which must be installed from the App Store, offers an alternative to Apple's Safari web browser. Although the Google app can act as a web browser, its main strength is its tight integration with the Google search engine. It is often a good choice for information searches on the web, but I've had occasional accessibility issues with the app. Try it and see how you get on. It has a very effective voice search feature built in to the app which avoids the need for VoiceOver dictation. Like all apps, it will start up where you last left it, so you may need to navigate back to the home page.
When the app starts up, you may hear "search field". If you don't hear this, slide your finger up a little from bottom centre of the screen where you may find a go to home button. Double tap this and you should hear "search field".
Voice search is often the most convenient and effective tool. Swipe right once to the the lens button. This is a powerful tool for identifying objects that you point your iPhone camera at but is unfortunately not great with VoiceOver. So swipe right once more to the voice search button. Think first what you want to search for, double tap, wait for the ping, speak and be silent until there is another ping to indicate that voice search has stopped listening. You may then hear a spoken response to your search request. Whether or not there was a spoken response, you can now explore the results that Google has turned up. I often prefer to do this by sliding my finger very slowly down the screen to hear what is under my finger. If I find a link of interest, I lift my finger and double tap to follow the link. You can, of course, use any method of your choice to explore the contents of the screen. You will find some suggestions in my notes on Safari. Because Google makes its money through advertising, you may have to travel a way down the list of results. For example, a search for Calibre talking books results in several advertisements for Audible ahead of the link to Calibre's web site.
When you follow a web link in the Google app, you will use the browser built in to the Google app and not Safari. The browser has a back button at bottom left, as in Safari. If you prefer to browse in Safari after searching in the Google app, you will find a share button in the bottom row of buttons in the Google browser. Double tap and swipe right until you reach the Open in Safari button and then double tap to view the web page in Safari.
I'd welcome your feedback on whether you find using the Google app has significant advantages or disadvantages over staying in Safari.