How can I check if Salesforce Org is affected with the Salesforce log4j vulnerability?

Salesforce log4j affected products and the status of mitigation have been posted in the Knowledge Article Apache Log4j2 vulnerability. They'll likely add more when/if they find more that have been affected. Conversation also continues on the Trailblazer thread OP linked to in their original question.

To directly answer your question, it doesn't look like you'll be able to specifically see if your particular org has been affected outside of checking that table in the link to the KA. A lot of them give the status as to what's being patched, others do say to contact Customer Support if you use that particular product (the current ones that say that are on-prem products).

That said, Salesforce has made it very clear that they will reach out to affected customers if they find evidence that their data has been accessed: As part of our continuous detection and monitoring systems, we have implemented detection and monitoring to alert for any potential exploitation attempts. If Salesforce becomes aware of unauthorised access to Customer Data, we will notify impacted customers without undue delay.