My understanding is that the OSB creates a responsibility for Ofcom to create a regulatory system for discouraging online harms. Has Ofcom actually said what these regulations will be? Is there any reason to expect them to be as dystopian as you predict? The interim codes of practice that the government published don't even apply at all to individuals. They also acknowledge that smaller companies should not be expect…
The bill itself doesn't appear to exempt anyone. From Taylor Wessing: "[following amendments] The OSB continues to apply to any service that enables content generated, uploaded or shared by one user to be encountered by another user (user-to-user services) or that allows users to search more than one website or database (search services)."
My point is that there is no reason to think the regulations that eventually come into force for services which aren't exempted will be as ridiculous as you suggest.
I agree that the OSB gives Ofcom the power to regulate Minecraft servers, but those regulations must be reasonable and proportionate so I don't believe that it will affect a private individual running a private server, as you appeared to suggest.