I dunno how I feel about basing the structure of the Federation government on the number of floors of one building. It's a little tail wagging the dog.
I mean, the structure of the Federation government in the novel continuity and the internal structure of the Palais is mostly based off of the novel Articles of the Federation; I'm pretty sure @KRAD didn't come up with the internal layout of the Palais first and then base the novel around that.

I mean, where's the real power? With the president in his penthouse offices at the tippy top of the royal palais? (Not necessarily but optics matter. Especially when this is all fake, isn't beholden to historic or logistical concerns, and can be anything.) Do councillors have any real power or are they more ceremonial (put'em in steerage on the lower floors with the press corps) and the real power (and larger staffs) with the ambassadors?
Well, Articles establishes that the Federation President and Federation Council share power. There's less of a division of powers than you find in the U.S. presidential system -- the Federation President regularly serves as the presiding officer of sessions of the full Council and has the option of serving as presiding officer over sessions of the committees (called sub-councils); the President appoints Councillors to the different sub-councils with the confirmation of the full Council; the President may veto an Act of Council, but the Council may override the President's veto; the security committee (called the Security Council) has the legal right to issue binding orders to Starfleet in addition to the President being the commander-in-chief of all Federation forces; the President appoints ambassadors but they must be confirmed by the Council; etc.
Broadly speaking, the President does appear to set the agenda in foreign policy, but they need to get the Council's support for major decisions, and the Council could vote to set a new policy by law if a majority strongly disagree with the President. It also appears to be an uncodified constitutional norm that the President will also solicit the advice of relevant Councillors for a given issue, bringing them into all the relevant meetings and treating them as a co-equal adviser with their own staff.
As with all legislatures, a unified Council ultimately has more power than the President, but it is rare for a Council to act with that kind of unanimity. One of the subplots in Articles featured the Council deciding to gum up the works and bring most of the President's business to a halt because she had insulted their loyalty to the Federation's foundational principles for having ratified a trade agreement with a slaver planet during the Dominion War. This broad principle, that a unified legislature can basically render the executive powerless if it wants to, is true of most constitutional republics.
If the power is with the Council, maybe their staffs are mostly offsite? Pretty easy to do with those flash transporters we saw on PIC. Staffers could be doing West Wing-like walk & talks from room to room in buildings all over the planet. Plus in the real world, post-COVID, we may see workplaces and HQ's being far less centralized. Maybe the Palais is where they convene to discuss and vote.
I could certainly imagine that housing Council staff in buildings located elsewhere wouldn't be that big of an obstacle in a Federation with routine teleportation. I doubt that the flash transporters existed in the 2370s though -- I think that is an innovation of the 2390s. Nonetheless, textually, Articles established that Council staff are housed in the Palais, at least as of 2380.
Or maybe the councillors don't need nearly as much staff as we might imagine. It's the distant future after all. Nix the floor with the typing bank or the phone operators or schedulers or that whatever else might be critical today.
As a former Congressional intern who served both in a House of Representatives office and a U.S. Senate office, I can confirm to you right now that there is no "typing bank" (everyone knows how to type), and that there probably wouldn't be one in the Star Trek Universe anyway, since writing is usually dictated to a computer by voice. A typical United States Representative's office consists of, from the top of the hierarchy down: a chief of staff, a legislative director, a press liaison, a scheduler, 2-3 legislative assistants, 3-4 legislative correspondents, 1-2 staff assistants, and however many unpaid interns they can con into working for free. So usually something like 15 people. If I'm remembering the Senate office composition, it was: a chief of staff; a deputy chief of staff; an assistant to the chief of staff; a legislative director; 3-4 legislative assistants; 3-4 legislative correspondents; a press liaison; a deputy press liaison; a network administrator; 2 staff assistants; and again, however many unpaid interns they could con into working for free. Something in the area of 20-25 people.
While a Federation Councillor would presumably be spared the 4-6 hours per day spent fundraising by Members of the United States Congress today, I'm afraid I don't realistically see a legislator of an interstellar union encompassing over 150 Member States (some with multiple planets under their own jurisdiction) realistically being called upon to do less genuine legislative work than contemporary legislators. It's almost a certainty that there would be too many issues coming under the Council's purview for any Councillor to develop meaningful expertise in any but one or two of them, and the needs of constituents to be able to contact and lobby their Councillors would be exponentially larger than in real life today. I could, with some suspension of disbelief, plausibly imagine that Federation Councillor would have a staff no larger than a real-life United States Senator; I can imagine them having a staff the size of a typical United States Representative if I squint. But I absolutely cannot imagine that a Federation Councillor would have less than 15 staffers at minimum.
Besides the councillor and their advisors, maybe most other staff work is automated. Wasn't that the idea behind there being fewer work stations on the Enterprise-D bridge?
The kinds of staff work you're talking about it generally not the sort of thing that can be automated. Most of it has to do with responding to constituent calls and messages, soliciting and responding to journalists, developing and maintaining relationships with other Members' offices, developing and maintaining relationships with stakeholders on important topics, etc. It's mostly hands-on work that requires a sentient entity.
I don't think I like the idea of the Council and the President both being in the same crosshairs. One photon torpedo and they're sending out Case Orange and scrambling to swear in the Secretary of Education.
I mean, I can't imagine that there isn't a giant deflector shield over Paris at all times, and if the Federation has any goddamn sense post-Wolf 359, there's probably always at least one dedicated fleet in orbit of Earth and another deployed in patrol of the rest of the Sol system, and that's not mentioning orbital defenses (both automated satellites and space stations) and ground-based defenses.
Like, even when the Breen Militia attacked Earth in 2375, there's no evidence from DS9: "The Changing Face of Evil" or the Tales of the Dominion War short story "Eleven Hours Out" that they were able to hit the Palais. So I'd say the Palais's defense systems are probably more than up to the task of protecting both the Council and the President.
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