can you back up phone while it's unresponsive?

Can an iPhone be backed up (on the cloud) while it's unresponsive but showing activity on the screen? It's not responding to touch and when I tried to turn it off it froze on the screen that shows "slide to power off" (it's unresponsive to touch).

I prefer not to do a hard reboot which in past iPhones resulted in losing photos and videos that are not backed up. I have data on my phone that is not backed up due to iCloud reaching capacity (2 TB) and Apple doesn't offer a larger plan.

(and Apple doesn't make it easy to move photos from iCloud to other apps such as Amazon or Google Drive, and there are issues with the integrity of files, perhaps due to Live photos).

When my phone froze, I logged into iCloud on my Mac to make room, using the cumbersome method of downloading pics/vids to my Mac in batches then uploading them to other services like Google Drive.

Even after clearing out several GB, I don't see the recent weeks of photos and videos that are stored only on my phone which means they are not backed up on the iCloud. I'm trying to see if there's a way to somehow back up those items from my phone using iCloud on my Mac.

If anyone can help, please share. Thank you.

Also, since iCloud is limited to 2TB, I am thinking of returning to Samsung where you simply swap out storage chips when they get full. It's not ideal, but I don't want to be in this situation again (and all my iPhones die within a year or two without warning and without physical damage - I use the best cases and protection and treat them so well, yet they die due to technical issues internally).

Many thanks. Hope this helps others experiencing the same issues.