I've been through a few of these generation handoffs, both as a buyer and sitting on the vendor side at a previous job, and the pattern is pretty consistent. The big flagship part gets announced first with a datasheet because it's what makes headlines, but actual orderable volume on that top part is tiny for the first couple of quarters. The mid-range parts, wich is where your money usually goes, show up 12 to 18 months after the announcement, sometimes longer. And even when the orderable part number exists, early allocation goes to the big accounts first. If your lead times are already painful, jumping to a brand new family makes that worse, not better, because new silicon always has allocation problems in year one. On the tools: yes, plan on them being rough. First releases of a toolchain supporting new silicon tend to have fit and timing quirks, incomplete IP, and bugs that don't get cleaned up until a couple of point releases. If you're spinning up a fresh project with a hard deadline, doing it on a mature toolchain with a part that's been shipping for a year or more is a much calmer experience. Early adopters on new families are basically unpaid beta testers, and that's fine if your schedule has slack. Yours doesn't sound like it does.
The other thing people forget is pricing. New generation parts launch at a premium and the previous generation gets cheaper as the vendor pushes the new stuff. If your design fits comfortably in an Agilex 5, you're likely to get a better deal on it now than you would have a year ago, and you'll actually have boards in hand.
My rule after getting burned once: never delay a real project for an announced part unless that part has a specific feature you cannot get anywhere else. A name and a slide is not a product. If the new family turns out great, your next project can use it, and by then the tools will actually work. Ask your manager the simple version of the question: does the project need anything the Agilex 5 can't do? If the answer is no, order it and stop worrying about it.