It's been asked in a few places that the old civ alert mechanism should be added back to the UI, so I'll just quickly reiterate.
Utilizing burrow assignment is both extremely cumbersome to manage and only has limited effectiveness, whereas the old civ alert burrow limitation was both simple to setup and enact. Having the game automatically limit civilians to pre-selected burrows is just simpler to conceptualize and enact than making a mega-burrow that you have to manually select for everyone and toggle on and off on the burrow level. Even just having a general "RED ALERT" button on the UI to toggle an emergency burrow limitation on and off would be a huge upgrade to the current workaround.
But since it's possible the feature is getting remade anyway to work with the new UI, here's a suggestion for a new system to supercede the old alert system.
Fortress Alert Level
Instead of the old system where the squad-level orders and alerts are mixed, separate the two and make orders part of the alerts. Squads have their own standing orders (which is what we have now) that they follow normally if nothing else comes up, and then you have actual fortress-wide alert levels that apply to the whole fortress, potentially both overriding standing orders and restricting civilians to burrows set in the alert level. Alerts could either have an "As you were" order for squads so they follow their standing orders, which is what the basic "No Alert" level would be for everyone, or separate orders that override the standing ones for the given squad. This way, you could have several different alert states for different situations. Manually set orders from the squad menu, like "Kill X", would override both the standing orders and alert orders, of course.
For example, you could have a general emergency order which limits civilians to the fortress proper only and orders defenders to all the entrances, a surface alert that limits civilians to the underground burrows while sending defenders to the surface entrances, separate cavern alerts for each cavern layer that limits civilians to the fortress and the surface while sending defenders to the appropriate cavern entrance, and a "yellow alert" of sorts where the squads start guarding the entrances and patrolling the fortress for thieves or assassins (if those ever get added to fortress mode) without limiting civilian movement.
For an example of what the UI could look like, imagine something like the old Evil Genius game with the alert level shown in the lower right next to the squad button. Pressing it would open a list of alert levels, a checkmark on the one currently toggled on and edit buttons on all of them. Editing an alert would look somewhat similar to the current squad order screens, but the first item shown in the list of squads should instead be the civilian burrow settings, and choosing what burrows to limit the civilians to could be done either by a list of burrows or by clicking the wanted burrows on the map.
The system is changed. Burrows are not for alerts any more. Not sure what they're good for, I guess for rationalizing dwarves day-to-day movements. As I only used them for alerts, I haven't exploded what good that does.
An alert is instead done by the labor settings. You have multiple settings that can make dwarves go inside the fort.
What I do is
-change fishing, plant gathering, woodcutting to "nobody does this."
-change stuff like cleaning floors and reload traps to "don't do during invasions."
So instead of having a general alert, you have like 5 different job settings you need to change. You can also tell them to ignore dead bodies and blood on floors and ammo on the ground and so on.
I personally find the new system MUCH better.
Like if reloading traps and cleaning floor is safe because traps and dirty floors are in a protected area but fishing us not, then I can keep doing the traps and floors and just close down the fishing.
It's far superior than the old "close down everything-alert". The old alert system also forced dwaves that were mining in perfect safety 20 levels down to run to the tavern. In the new system, they can just mine on.
Now, you could argue that to make it easier for people to discover this, there could be an alert button that changed the labor settings to the most typical stuff you'd want for an alert. But I think this would make people not explore the tabs in the labor setings.
At most, maybe the tab for the relevant labor settings should be renamed so it's totally obvious that the tab is important. Like "labor settings for emergencies" or something like that? Or you could get a prompt screen "You've got your first invasion, so you wanna check out tabs XYZ to save dwarves."
I think however most of us old players just miss those yabs as we're accustomed to think like "an invasion happens, so it's burrows-time".
New players probably don't have this UI-problem, as they wouldn't even look for burrows when there's an invasion.
It makes sense to me than when dwarves are doing labor that put them in harms way, you'd look around in the labor settings to find a way to get them to safety.
So I think it's basically fine as it is.