My understanding is that the "encourages" part relates to agencies that are independent and are therefore not directly under the control of the president. He therefore cannot directly order them to do anything.
However, from what I could gather from news interviews, this has not been published without the collaboration from those agencies, who in general are on board with the changes.
Correct, the President is actually fairly limited in how much control they exert over regulatory agencies -- such agencies are created by Congress, commissioners are nominated by the President and confirmed by Congress, and commissioners report back to Congress.
It's an executive order, there is only so much the President can mandate outside of the organizations he controls. Look at most of Trump's presidency, feckless EO's that in the end were reversed anyway or were blocked by a court. My guess is that the goal here is to have the regulating authorities be "encouraged" to put the screws to some of these big-X companies. In other words, have them set their policies based on the general direction given by the President. I think that's probably normal operation.
A more cynical view is that the goal is to make it seem like the administration is trying to follow through with some campaign promises while not doing much of legwork to actually do it.
It takes very little to issue an EO. It takes more to work with colleagues in congress to actually implement some of the stuff laid out here. Biden's predecessor really laid the framework here and turned it into an artform - issue a worthless EO, get a great photo op and some feel good stories in the media, then everyone forgets why they can't figure out hospital prices in a few weeks again.
For some more context, it is within Biden's power to appoint an assistant attorney general for antitrust, but as of last week, he still hasn't [0]. I'm not sure how serious this rhetoric around strengthening antitrust guidance really is, in light of that.
I'd love to be proven wrong, but I think this administration has earned my skepticism. Time will tell.
However, from what I could gather from news interviews, this has not been published without the collaboration from those agencies, who in general are on board with the changes.