Google backup won't work. You'll have to manually move everything over the first time by reinstalling apps and moving data over through USB, Cloud storage, etc. There is a backup option on GrapheneOS that other custom Android OS's use as well called SeedVault, but its known to have some issues and it's on the GrapheneOS timeline to replace it.
Make a list of all your installed apps. Maybe take some screenshots if you want to remember how you currently have things laid out if you want to replicate it on GrapheneOS.
Make sure you have the right login details in your password manager for any online apps.
Export backups from any app that only stores data/settings locally and copy those exports to an external storage device or your computer so you can easily import them afterwards. Most FOSS apps offer this.
Copy all of your other local files and media stored in internal storage to an external storage device. Make sure to retain the folder structure when you copy stuff over since it may be important for some apps.
If you do have anything synced, such as WhatsApp encrypted Cloud backups, remember to sync them one last time before you switch over so you don't lose any data.
Backup your SMS/MMS and call log using a third-party app. There are some open-source ways to do this, by imho, the most reliable one is still SMS Backup & Restore on the Play Store. It's been around for ages. You can just save the backup locally and move the backup files to external storage like everything else. Make sure to select the option for attachments and media in advanced options if you want those brought over too, though this will increase the size of the backup depending on how many media attachments you have in your message history. RCS messages will be brought over as MMS messages.
If you don't plan to use Google Messages RCS on GrapheneOS, disenroll your number to avoid messages potentially not going through.
Confirm that you either have a physical SIM card or the means to contact your carrier to request a new eSIM just in case it doesn't automatically appear after switching.
If you've made any preference/convenience changes to settings, screenshot them so you can remember how to replicate it on GrapheneOS if you so wish.
When everything is backed up and ready, begin the installation process which will delete everything on your phone. I would budget at least 2 hours to give yourself enough time to complete the installation and enough time to setup your phone so it's mostly usable.
Play around with settings, user profiles, and install sandbox play services and play store if you want them. If you're unfamiliar, I'd highly suggest looking into these things before you install so you don't waste time or feel overwhelmed. Depending on how high your threat model is, there are also additional steps you may choose to take during initial setup that will forfeit convenience in favor of privacy.
If you intend to use things that rely on specific Google apps, install the Google Apps first since some apps expect google apps to be pre-installed. For example, if you intend to use encrypted Google Drive backups for WhatsApp, install Google Drive first and login before insgallinf whatsapp. The same goes for Google Contacts if you desire google contact syncing. You may need to log out of these apps and back in once or twice.
Begin installing other apps through your method of choice with/without Play services. There's a lot of advice on here about this as it pertains to privacy and security. You may use this opportunity to set increased privacy controls on apps such as denying network access, restricting sensors, or using contact/storage scopes.
Move over all your data from external storage. Begin logging into apps and importing backups into corresponding apps.
Restore your messages and call logs using SMS backup & restore. Depending on how large your backup is, this could take several hours. So, I'd do it at night.
If something doesn't appear to work right away, search this forum for a potential solution or ask a question.
Enjoy GrapheneOS