That's a surprise. I had always heard Crusade was a detailed set of rules where you play from 500 points to a full 2000-3000 point game at the end over the course of a year (assuming you play once a month).
It's assumed people do that, not specified. You can set the interval however you want, along with army points caps.
The specifics vary from crusade to crusade. One might be about area control, another might have a branching path that determines the outcome.
Not really, it's up to people to do that on their own and that's one of the problems. Yes there's a bunch of lore in the book of things that other factions are doing, not stuff that you're doing. It'd be like getting a splatbook with some character options and reading about and adventure of Drizz't or something, not an actual campaign itself. It's got missions as well of course, but they aren't faction specific, there's no narrative to go with them beyond a 1-2 sentence description.
With the intention of growing your collection throughout.
This would make sense but isn't specifically the case.
There are even faction specific objectives and upgrades.
There are, and generic versions depending on which crusade book you're using(and if the codex for your army is actually out yet). that are themed to go along with that book. The main part about the crusade books is really whatever the big "mechanic" is, like the blackstone fragments being an additional currency(like xp, campaign points, requisition points, etc.) to track and providing additional upgrades separate from the traits and relics.
Hearing it talked about online, I was expecting something grander. Almost like DnD where units gain levels and names, and while I imagine the 3000 point finale would be a bitch to play, the build up where units are recruited, lost, and replaced, while a few choice veterans make it through either as elite bad arses or as war weary shadows of their former selves.
It is, so long as the organizer comes up with a narrative that's worth a shit and can organize the games into something people are interested in playing. Another major problem here is that it is like D&D and it scares people off. They have to track xp for units, you need to get at least a game in depending on how often you're scheduled to play(weekly, bi-weekly, monthly, whatever) and people hate commitments even if it's 1 saturday a month. Just like D&D. Hell, even the tracking isn't super hard because there's spreadsheets and websites that help but people act like adding single digit numbers is difficult even when the spreadsheet does the actual math for you.
In my last crusade league(Tyrannic War, the one from the start of 10th) we had teams kind of acting as super-factions, 3 out of the 16 players dropped before it even started(just never showed up). And it was planned to go from 500-1500 point armies(supply is a whole separate thing, imagine it like a sideboard up to a larger number of points, which you can even spend XP on increasing but doesn't increase your army point count per game), with 1 game played in store for XP every other Saturday, and players able to organize games with eachother(so long as you weren't teammates) any other time but only 1 of those games would count for army xp(keep people from snowballing wins, but allow people to get in make-up games if they missed something) and only the Saturday games would count toward gaining territory on the map. After about 4 weeks another handful dropped, and by the end of the league after 12 weeks we were down to 6 players and even then only half of them were willing to find the time during the 2 week intervals to get another game in. Because it was such a shit show, we just had the finale be a giant 3v3 at 1500 points per player(so 4500 per side, but it actually went pretty quick because you've got 3 people moving their army all at once, resolving attacks, etc.) with a narrative of needing to defend objectives at the center of the board so we could have a huge silly game and get it over with and of the people that up and left the league(usually without notice leaving us starting late waiting for people to arrive) I've only ever seen I think 2 again in the year since? No idea wtf happened to the rest.