Can I set Google Photos as my default cloud photo backup?

There is a Google Photos app for iOS. If you run it, it will ask permission to access your entire Camera Roll. I'm guessing this is for the purpose of synchronizing the Camera Roll with Google Photos (in the Google cloud).

Although you can turn iCloud Photos and Google Photos on at the same time, I've read that it may not be a good idea. IIRC, the danger is that if you run out of Google cloud space, and you start to delete photos "from Google Photos" to free up Google cloud space, that'll also be taken as a request to delete them from iCloud Photos, and you will wind up deleting them everywhere.

https://lifehacker.com/why-you-should-un-sync-google-and-apple-photos-1848762896

I.e., if you don't have a clear model in your head of how both systems work, and how they might interact, then it might be a bit too easy to destroy your data (even if the ultimate cause was pilot error).

This search brings up links to several Google Photos Help articles tagged with "iPhone & iPad", including a "Get started with Google Photos" article and a "Back up photos & videos" one.

https://support.google.com/photos/search?q=iPhone

Here's Google Guidebook for setting up Google Photos on an iPhone:

https://guidebooks.google.com/iphone/photos/how-to-setup-google-photos-iphone

This article talks about a tool that Apple provides for transferring photos from iCloud Photos to Google Photos.

https://www.cnbc.com/2021/03/03/how-to-copy-your-apple-photos-to-google-photos.html

It sounds like you don't have any photos in iCloud Photos (yet).

I'm sure that if you do a Google search on the subject of using Google Photos on the iPhone, you can find more.

It's easy to set up your phone not to sync photos to iCloud. Most iPhone users want to turn it (or leave it) on – but this support article will show you where the switch is, so you can go in and make sure that it is turned off.

Set up and use iCloud Photos - Apple Support

You can turn off iCloud Photos and still use iCloud synchronization for other things such as Contacts, Calendars, and iCloud Drive.

iCloud User Guide - Apple Support

Sign in to iCloud on all your devices - Apple Support

If you connect to your e-mail provider through IMAP, your mail should synchronize between devices whether you have iCloud synchronization for Mail turned on, or not.

You can connect to mail, contacts, and calendar accounts from various services (Google being one that's easy to set up):

Set up mail, contacts, and calendar accounts on iPhone - Apple Support

I would strongly recommend that you turn on the Find My services and keep them turned on. If you misplace or lose your iPhone, and Find My was turned on, you may be able to find it by signing into the iCloud Web interface, and looking for it on a map, or asking it to play a sound (if the map shows, or you know, that it is nearby).

Set up Find My on your iPhone, iPad, iPod touch, or Mac - Apple Support

If your iPhone, iPad, or iPod touch is lost or stolen - Apple Support

If it is stolen, you can mark it as Lost, even remotely give a command to erase it (while leaving it Activation Locked), thus "bricking" it and making it worthless to the thief. (Just don't remove it from your list of trusted devices as outlined in Step 7 of the second support article, unless you want to let the thief "make the phone their own".)