I allowed all permissions for notifications, but they still didn't work.
I did a bunch of Googling but the only suggestions (allow permissions, clear cache, restart phone) didn't solve the problem. So I'm posting this solution for future Googlers.
The problem is that popup notifications don't happen for the Google Clock app, for its alarms or timers. This is due to those notifications being suppressed by having the Brief notification popup style enabled, which is enabled by default as a system setting. The Clock app only supports the Detailed style, so the Brief style setting keeps them from showing.
The solution is to deselect the Clock app under "Apps to show as brief", and this allows the popups to happen. You could also change the system popup style to Detailed, to change this setting for all apps.
BTW, the Samsung Clock app doesn't seem to have this problem, maybe due to it using its own custom popups at the bottom of the screen, rather than using the system popups.
Extra Tip
If you want your Brief popups to stay onscreen longer than 3 seconds, you can adjust that under the "Edge lighting style" setting, on the Advanced tab, where you can select 4 or 5 seconds, which helps. You can leave the Effect tab set to None, and the edge lighting won't be enabled. Strange that they hide the popup duration setting in there.
And Another Tip
If the Google Clock is not appearing over your lock screen when an alarm goes off, to show you the Snooze or Stop swipe options, then you need to grant permission for it to do that. You can do that in Settings > Apps > dot menu > Special access > Full screen alerts > Clock.
