> “Congress shall make no law respecting an establishment of religion.”

Right

> It literally just says the federal government can’t interfere with the official state churches, which were called “established churches” (and that the federal government couldn’t establish a church itself).

You are down selecting only half of what the simple statement says. You are making a distinction of “interference” not in the text.

No religious establishment based “interference”, yes that is consistent with the phrase, but less general than the actual phrase which includes no such restriction.

It also is consistent with no establishment based “preference”.

“No law…” is the actual clear, simpler, and more general wording.