(I’m in the process of renewing my US passport, so I’m immersed in the forms and guidance at the moment.)
I don’t think the US plans to add a new “gender” field on the passport. The officials announcing and implementing the changes seem to be using “sex marker” and “gender marker” interchangeably, and the media is running with that rather than doing real investigative reporting. Currently there is a field for “Sex” on both the application forms and the actual passport, no “gender” field, and yet the new guidance advises how to fill out the “existing gender marker” or “change the gender printed on your passport”. So all this “adding a third gender marker” - pretty sure it just means adding an X to the allowed values under the existing SEX field.
The change has already been made to allow the existing SEX marker to be set as or changed to M or F based purely on reporting by the applicant. This isn't only for "transgender Americans"; anyone entitled to a US passport has the same opportunity. The next change is most likely to introduce X (and possibly additional values) for the SEX marker, still on a self-description basis. I don’t think the SEX field will be removed unless/until the ICOA make a change in their requirements/recommendations, but there may be some leeway with additional indicators besides X/O (which other countries already use) as long as their purpose is clear.
RE the need for a SEX marker on a passport at all - there was a case in 2018 in which an applicant sued the US State Department and their local passport office for refusing to issue a passport without a SEX of M or F (they’d requested X, or nothing). The applicant lost, but the reasons the government put forth for needing the sex marker and for restricting it to M/F seemed to be mainly administrative/technical rather than real-life-practical. Basically they argued that sex is used as an element in verifying identity and an individual should have all related identifiers matching across different pieces of documentation and different US government departments. Discrepancies of any characteristic used as part of “identification” would cause technical issues, increase workload, and pose security and/or fraud risks. There doesn’t seem to be any substantial reason stated why sex specifically needs to be part of the set of characteristics used, except that it is already in use and so needs analysis to make sure there are no unexpected negative impacts if changed.
That said, all of that analysis is US-focused; the US can’t control (or necessarily predict) how other countries’ border control or law enforcement or even civil society (for example, a hostel checking a foreign visitor’s passport to verify a reservation for an all-male or all-female shared dormitory) will use the info, and whether there might be complications for the bearer in the case of a sex marker which some foreign official or agency perceives as inaccurate or questionable or even fraudulent.
Also, some US states already issue birth certificates with SEX = X not just in cases of an adult requesting a change but also for newborns - so breaking the link between the passport SEX field and any documentation technically closes the gap for anyone who genuinely has no official record of a male or female sex in that they could simply choose at random. (Which I’m sure is not much comfort to people in the situation, but does give the US government some legal breathing room before adding X.)