You're working with both Outlook (desktop) and Outlook Web App (OWA) and therefore want to use the same default signature in both clients.
If your Outlook Web App (OWA) email signature is incomplete, you have reached the character limit for OWA.
With Exchange Server on-premises, Microsoft enforced an 8KB character limit in OWA email signature settings.
We have not yet seen limitations with Exchange Server online (Office 365).
If you see an incomplete email signature in OWA, please reach out to us, and we'll help check acc. to our Best Practices.