Short answer: Poster 7 is essentially a reiteration of "the regulations" and thus "the law". As for photography, "it depends".
Poster 7 is nearly word-for-word identical to the regulations in 39 CFR § 232.1, enacted in 1972, by the powers delegated to the Postal Service by Congress in 39 USC § 401. "Nearly".
The regulation refers to "news purposes", not "commercial use". When is photographing a person in a post office lobby actually a qualified "news purpose"? If the photographer tells people it's for his or her "personal use", does that defeat the claim that it is a "news purpose"? Clearly it is illegal (like any activity inside postal property) once the "authorized personnel" tell you to stop, risking up to a $10,000 fine and 30 days in federal prison, in addition to the immediate state trespassing charge and penalties.
The list of authorized "news purposes" photography locations ends with "auditoriums when used for public meetings". If they meant to include only "lobbies ... when used for public meetings", they should have put a comma in front of "when". Otherwise the succeeding limitation grammatically and logically only applies to "auditoriums". A court may apply the rules of statutory interpretations, such as noscitur a sociis, differently.
Unlike Poster 7, the regulation 39 CFR § 232/1(i) and the original regulation at 37 FR 24347, Nov 16, 1972, have the limitations listed in "Except as prohibited by official signs [etc]..." BEFORE the term "photographs for news purposes may be taken [in authorized public areas]...", rather than after. This would seem to more clearly state that photographs for "news purposes" are permitted unless specifically prohibited (by signs, orders, instructions), subject to "permission" for "other photographs".
As for relevant "court" interpretation, I found a federal opinion that comes very close to answering this question, at least as related to an alleged violation of a "First Amendment right" to PLAY a recorded message in the post office lobby, after someone did so, in violation of 39 CFR § 232, refused to leave when told, and was arrested for trespassing. It's not even binding precedent in New York, but at least it shows that court's thinking.
Held: Claims dismissed against US Post Office in lawsuit for damages and injunction arising from alleged illegal trespassing arrest. (among other things).
In short:
"A First Amendment claim that the government is impermissibly restricting a speaker's access to government property is controlled by the now-familiar tripartite forum analysis.... The extent to which the Government can control access depends on the nature of the relevant forum. ... Generally speaking, when the state reserves property for its `specific official uses,' it remains nonpublic in character. ... There is little question that the Postal Service is essentially a commercial enterprise.... [I]t is also well settled that the government need not permit all forms of speech on property that it owns and controls. ... The court further finds that the interior of the Jordan, NY Post Office is a non-public forum with respect to which reasonable restrictions on speech may be imposed... In nonpublic fora, the government has wide latitude in regulation of speech, it may even be content-based as long as it is "reasonable" and "not an effort to suppress the speaker's activity due to disagreement with the speaker's view." [internal Supreme Court and 2d Cir. case citations omitted]
See, e.g., Moore v US Postal Service, in the NDNY federal district court, 01-CV-1609 Jan 13, 2005, where Mr Moore was "trespassed" from the post office and arrested by local police, after violations of several subsections in 39 CFR 232 inside the post office lobby, although not specifically 232.1(i) regarding "photography".
This information is only my personal view of this case excerpt and is not in any way intended as "legal advice", let alone a complete analysis of the actual issue of post office photography. If someone finds a contradictory case in another federal court, let alone the US Supreme Court, let us know! FWIW, USPS or DHS policy statements about whether or not to enforce rules like this are not "law" and thus irrelevant to the underlying question.