Can you provide some links to anything that supports that? Her antitrust philosophy is built on a hostility to business success as such so I don’t see why she would have any positive disposition to smaller businesses.
There are lots of different views about the goals of antitrust law and policy, but few (if any) are hostile to business. Khan is pro-business but also, broadly speaking, pro-dispersion of economic power within the economy. That means having fewer 'gatekeeper' firms which exercise power over key economic bottlenecks, and at the same time, a greater focus on helping smaller and medium sized businesses succeed.
For a concrete reference regarding small business, see this recent speech of hers [1,2].
The most recent NPR planet money podcast played their first episode on Ida Tarbell and Standard Oil, the old Bork episode on changing antitrust law enforcement then followed up with a half hour interview with Khan.
https://www.npr.org/podcasts/510289/planet-money
There’s arguments she makes for fair competition and for monopolies being capable of making anti consumer marketplace decisions. I assume that you are not saying there should not be anti trust or anti monopoly laws, that’s a different argument I think. She doesn’t say anything like what you are claiming here.