Some time ago, I sent a Form SS-4 (Application for Employer Identification Number) to the IRS, and later received a reply from the IRS containing the EIN. Recently, I discovered that the Form SS-4 I sent and the IRS' reply are somehow publicly available as a PDF download if one searches hard enough using a search engine. The form contains my full name, my EIN, and my signature. I used a third-party's address as my mailing address, so my home address is not leaked. Is this a cause for concern in terms of privacy, identity theft, etc.?
It's not a cause for concern in the sense that there's no way you can keep your EIN secret since there's many government entities (states, and FCC for example) that will provide your EIN to others if you're registered to do business with them or need them for licensing. Apparently tax fraud happens where people steal someone's EIN but all you can do is then try to prove to the IRS that you aren't responsible. Business EIN Tax Fraud
Your signature, I guess that might be something someone could copy but realistically, I don't think that the vast majority of places that accept signatures actually have a handwriting expert to verify that the signature is legit so a criminal could just make up a signature out of thin air. In the modern age of digital signatures (and rubber stamps) it's really hard to tell if a signature is legit or not just by looking at it. It's more like if someone uses a signature without authorization, it can be used as evidence of fraud against them at some future point in time. After whatever crime occurred.