If I’m getting a notice from Apple that my phone needs to be backed up, why don’t you give me the option of backing it up?

iCloud can be set to backup automatically in Settings->Account (top of settings)->iCloud->iCloud Backup

If you do not have enough space on iCloud for the backup, you can backup to a computer Mac or PC running iTunes or Finder.

See here: link-> How to back up your iPhone, iPad, and iPod touch - Apple Support

You can do a backup. Settings > [Your name] > iCloud > iCloud Backup > Back Up Now.