Doing an iCloud Restore usually causes problems. I have always set my iDevices up fresh and have never restored from iCloud - there genuinely is no reason to as all the important stuff like contacts/photos/messages etc automatically get backed up & will re-download when you set your iPhone up again as new.
Here's what I would do.
Sign into iCloud, clean up all your photos, contacts, text messages, mail, reminders, bookmarks, notes, iCloud Drive storage, etc.
Delete whatever backups you have in iCloud Settings (which will turn backups off), turn Backups back on and upload a fresh backup.
Once your data has been backed up, take screenshots of your home screen layout/apps so you know what apps you need to re-download & your preferred app layout.
Once you're confident you've saved everything important (I'm not responsible if you lose anything), go into reset and erase all content and settings. After this is done, turn off your iPhone
Next, (and most importantly) we need to do a fresh install of i0S 13.5.1 using recovery mode. This will completely wipe the iPhone's storage and re-install the latest version of i0S as fresh. You'll need a PC with iTunes or a Mac and your lightning cable. You can search for how to put your iPhone into recovery mode, but it basically consists of opening iTunes, plugging in your iPhone into the computer, and quickly pressing vol up, then vol down & finally holding the sleep/wake button. This will put your iPhone into restore mode and iTunes/Mac OS will prompt you to Restore & Update the phone.
Once the process is done, your phone will be fully factory reset and you can go through the normal setup process. After you sign into your Apple ID & when it asks you if you want to transfer any data, DO NOT RESTORE FROM A BACKUP OR TRANSFER DATA, just set it up as a new device. Your photos/contacts/bookmarks etc you backed up earlier will automatically appear anyway.
Once you're done with the setup process, re-download all your apps manually & set everything back up as you normally would. Your battery woes should be resolved.