Or do these limits only kick in for platforms above a certain size?

That's how it's in the EU, the DSA only applies to large providers. It's kinda like the fairness doctrine in broadcasting but in the digital domain, e.g. TikTok is currently in hot waters over the Romania elections because they did not take sufficient precautions to make sure that everything's fair and square.

And in that case, why would the same principle not apply?

Because size obliges. If I want to smelt some cans in my backyard I can just do that provided I have a "fireplace" -- which is just an area set up to be suitable to have a fire. If I want to build an industrial-scale aluminium smelter I have to get permits and everything. The public interest in the latter is much larger, that's why I have to jump through hoops and follow regulations.

(I can't burn garden waste though, gotta give it to the municipality to compost. A matter of waste of perfectly fine organic material and unnecessary emissions).

If I make sandwiches and people decide to eat my sandwiches then why should the government require me to follow basic health and safety.

Service offered to the general public should expect to be regulated.