Glad to have you here in the Community, @jp-chickenscratc.
Currently, the integration with Square is only available in QuickBooks Online via Sync with Square app. As a workaround, you can download your Square transaction into a CSV file and manually import them to your QuickBooks Self-Employed account.
Here's how:
1. Go to the Gear icon, then select Imports.
2. Select Import older transactions.
3. Click Browse and find the file you downloaded from your bank.
4. Follow the instructions onscreen to finish importing your data.
5. Select Continue to complete the import.
After importing the transactions, you can now review and categorize transactions to put them in your accounts.
Keep in touch if you need any more assistance with this, or there's something else I can do for you. I've got your back. Have a good day and keep safe.