Recently, I onboarded Cloudflare for a handful of websites in my portfolio. However, I've just received a notification from my hosting provider indicating an issue with re-issuing the SSL certificate.

The question remains, do I need to intervene in this scenario, or is the site currently leveraging a Cloudflare-issued certificate? Notably, I've configured my settings to utilize the Full (Strict) SSL/TLS encryption mode, which ostensibly should mitigate any potential certificate-related issues.

Given this setup, it's unclear whether the error notification necessitates any immediate action on my part, or if the site is already adequately secured via Cloudflare's certificate.

You're right to question whether the error notification from your hosting provider requires immediate attention. Given your setup with Cloudflare's Full (Strict) SSL/TLS encryption mode, it's likely that your site is already secured via Cloudflare's certificate. In this scenario, the notification might be a false alarm, and you might not need to intervene.
Cloudflare's certificate is probably taking precedence over your hosting provider's SSL certificate, effectively shielding your site from any potential certificate-related issues. However, to confirm, you should check your Cloudflare dashboard to ensure that the SSL certificate is indeed issued by Cloudflare and not your hosting provider. If it's the former, you can safely ignore the notification.

When configuring SSL/TLS encryption, you can opt for a Flexible setup, wherein Cloudflare autonomously provisions and manages the certificate, rendering any additional intervention on the hosting end obsolete. In this scenario, any errors that arise will merely manifest as innocuous informational notifications.

On the other hand, if you elect to implement a Full setup, your hosting provider will need to undertake the necessary configuration on their end, necessitating a more hands-on approach. This might involve collaborating with their technical support team to ensure seamless integration and mitigate potential compatibility issues.

Is Cloudflare presently leveraging its own SSL/TLS certificates, or would the implementation of a Let's Encrypt certificate for the same domain result in a redundant issuance, effectively creating a certificate duplication anomaly? I'd argue that we're dealing with a distinct certificate issuance, rather than a mere certificate cloning scenario.
Alternatively, are you provisioning server-side certificates via a different Certificate Authority (CA), such as GlobalSign or DigiCert, rather than relying on Let's Encrypt? It's essential to clarify this to avoid potential certificate conflicts and ensure a seamless SSL/TLS handshake.