The notification is designed to only appear in the "active" device. So if you're using your phone, the notification appears there. If your phone is locked, the notification goes to the watch. I find the mac notification a bit weird in this aspect, but the ones between iphone and apple watch will work as you describe.
More info here: https://support.apple.com/en-us/HT204791
Not OP, but it really depends on your lifestyle. I need to be connected most of the time because of my job and in case of family emergencies.
Before wearing an Apple Watch, I'll need to take out my phone to look at the notification and determine if it's important. By doing so, I may unlock the phone and do something else as well.
But with the apple watch, I'll glance at my wrist for the notification and see if it's important. If it's not important, I'll dismiss the notification and continue with whatever I'm doing. I'll only take out my phone to respond if it's truly important or require immediate attention.
Just this aspect makes me still be available for the important stuff but can put down/away my phone more often.
Apple Watch is not luxury, if I want luxury I'll be rocking my mechanical watches instead (which I do when I go to a more formal event/gathering).
That said, I use my Apple Watch for Apple Pay and as a filter for notifications to see if I need to respond immediately. Just these 2 features have already improved my life. The added bonus is the passive health tracking features that encourages me to move more.
The main benefit of AOD for me is when I need to glance at the time during meetings. I don't want to do the whole turning my wrist thing to "wake up" the display.
This is a "feature" that I always have with my mechanical watches and something that's essential to my workflow.
When there is a notification, I can use my apple watch to separate out notifications that I need to immediately respond (e.g. important message/call from work or family) vs ones I can take care of later without taking out my phone. Before having the apple watch, I have to take out my phone every time when there is a notification.
I also use Apple pay with the watch all the time without taking out my phone.
Both of these use cases works with non-cellular version as well. Of course you'll need your phone nearby or have wifi so you can receive messages, but it doesn't require you to have a cellular watch or have the cellular plan on the watch.
One time I had issue with getting mail notification on my watch, I have to go to the watch app on iphone > Mail > Accounts and login to my email accounts. Some of them shows "Sign in required" for some reason. After that the mail notification works perfectly on my watch.
Not sure if it's the same as your issue though.
More info about the double tap feature on series 9: https://support.apple.com/guide/watch/use-double-tap-to-perform-common-actions-apdabb7b275c/watchos
I want to like this watch face, but it's just too much information for me. At a glance I won't be able to tell what the things are and it'll take me more time to interpret the information. Maybe it'll be better if I give it enough time to get used to the layout.
Series 4 have been around for a while and if it's still on the original battery, the battery health is probably the issue. You may want to check the battery health of your series 4 and decide if you want to get a new battery or a newer watch.
I don't work for Apple, so can't say if it's just Apple gatekeeping features for higher-end watches or there is really a technical reason. However, I think you overthink too much about the keyboard feature. I'm using an S7 and I would only use the keyboard to do really short replies and will take out my phone for anything longer than a few words.
Love the milanese loop.
I'm a mechanical watch enthusiast and have a modest collection, but I've been mainly wearing my Apple watch after I got my first one. Love getting notifications and using Apple Pay with the Apple Watch. Now I only wear mechanical watches when I'm attending a more formal event or I know I'm going to meet other watch enthusiasts.