1. big colorful face but not a huge box around it
Most of the current smartwatches all follow the same pattern. They all have 1.4" displays, or close to that. The screens are small enough where pixel density and such is not really a problem. Max brightness, however, depends on what the manufacturer decides. Most, if not all, use some type of OLED display. In my experience, the LG Watch Sport and my current Diesel watch have extremely nice, vibrant displays. I'm sure that all of the current group of smartwatches are pretty equal as far as display goes.
2. thin with small bezels not huge like an old Casio
The LG Watch Style and some of the Ticwatches appear to have fairly small casings/bezels. You'll just have to look at the pictures on the Google website to compare the casing sizes.
3. full Wear OS and run lots of apps
All of the watches I've pointed you to run full Wear OS. It's just that some, like some of the Ticwatches, are also capable of running a less feature-rich, easier on the battery mode. It's entirely up to you whether or not you'd ever want to switch from the Wear Os to one of those lesser modes.
Apps running on the watch depend on the app developer. Most of Google's apps are accessible on the watch. There are quite a few other apps that run on Wear OS watches, but not every app in the Google Play Store will have a watch version. Basically, your watch will be a mirror of your drop-down notification shade on your phone, with a few handy apps and extras that you can install.
4. battery life
Battery life on Wear OS has always been an issue. All of the watches I've owned have, for the most part, lasted all day, but definietly need to be charged overnight. Things like heart rate sensors, gps, etc will drain the battery quickly if they are used. If you're only planning to use the watch for notifications, battery life will be ok for you, but you'll still have to charge daily/nightly.
My Polar watch is the exception. It gets two day battery life. It's the only watch that I've owned that could get that much out of the battery.
5. lag sucks so a new processor
All of the watches manufactured before August of 2018, or close to that, run the 2100 Snapdragon processor or an equivalent. Those processors, especially the 2100, were battery hogs, from what I've read. They could get somewhat bogged down or stutter, but not terribly so. The new 3100 processor is supposed to be a little kinder and gentler on the battery.
Here's an article about the new processor:
https://www.pcworld.com/article/3304371/mobile/snapdragon-wear-3100-wear-os.html
I'm sure there are more, but the ones I know off the top of my head that are using the new 3100 processor are Louis Vuitton Tambour Horizion, Montblanc Summit 2, and the newer Fossil watches.