Is there a setting so as when I swipe away a notification on iPhone/iPad or Apple Watch that when I go between devices I’m not bombarded with the same notifications I’ve already swiped away on the other device.
you would be correct in thinking that something is wrong on your devices.
a message swiped away from one device should remove the notification from all devices.
but, the bad news is that there is no one setting that controls this.
the way that it is intended to work, and, works this way on my devices is that apple knows which of your devices you are actively using due to features that enable continuity and synchronization across the apple ecosystem, provided you are signed in with the same Apple ID.
apple sends the message to that device that i am currently working on.
the primary technologies that allow this are Handoff and iCloud, through bluetooth and internet.
apple primarily uses local processing to ascertain which device you are currently using.
for many continuity features, the data exchange happens locally between your own devices over Wi-Fi and Bluetooth, without being sent to apple's servers.
so, in your case, the things to look at:
1 are all devices signed in using the exact same apple account iD
2 are all devices signed in to iCloud
3 are all devices using a display time out that is set to something other than "never" or an hours-long period
4 are Messages and FaceTime also set to the exact same apple account login?
5 are all devices signed in to the internet
6 are are all devices that you signed into being shown in the devices section of iCloud ?
7 are you working on two devices at the same time and both devices are set to a long time out duration?
8 are some devices in an especially weak area for internet or bluetooth reception
9 are some devices out of bluetooth range due to concrete walls or something
10 check your Notifications setting on all your devices for each app and make sure they are set to what you need, hopefully without any inconsistent settings between devices.
11 make sure you have consistent Focus settings between devices. Focus is the area that has caused me some notification issues due my improper setting of parameters
12 shut down and reboot all your devices. then restart them one by one.
13 on yr iPhone, go to Settings/Privacy & Security / System Services / (i have turned on many/most of these settings (such as Networking and Wireless) be aware that you will need to understand the privacy risk of turning on any of these settings.
i have a Watch, Mac, and an iPhone. and especially with iOS/WatchOS/macOS 26, notifications problems have actually become zero for me.
its pretty amazing that apple has figured out a way within 2 or 3 seconds for my devices to know which one i need the notification on. if i am working on my mac, and i walk into the next room with my Watch on, the Notifications come to my Watch. if i am out running using Workout, the notifications that i have allowed through in Focus come to my Watch, but don't go to my iPhone which is with me in my pocket (i have the iPhone Air). etc etc. its really implemented well.