[Updated and corrected 27th December 2019]
Sorry for the late reply. It is so late that numerous new sports watches have been released in the meantime:
The Fitbit Versa 2 now supports an always-on mode, but it only has two buttons; most stuff is handled by the touchscreen, which is not a good idea.
Same for Garmin Vivoactive 3&4 / Venu and Apple Watch 5: These are Touchscreen watches (and even Apple now supports always-on, although you can expect barely one day of battery live), and thus not really suitable.
But on to my short and incomplete guide. This summarizes information from manuals, YouTube videos, and various reviews.
The Coros Apex (220€-250€ in Germany) is a Triathlon watch. Its has interval training and supports triathlon, but its other functions are very limited.
The Suunto 5 (220€-250€) even has a dedicated Badminton profile. (Not that it’s any special, on other watches you can just create a Badminton profile should you need one.) The watch supports simple interval training, à la 3x10s seconds. The display is rather small though, and the notification support is pretty sparse.
The Polar Vantage M (~200€) has a larger screen and simple interval training as well, but no detailed training plans.
The Garmin Forerunner 45 (~160€) is similar to the Suunto 5 in features: Simple interval training configurable on the watch, and basic notification features.
The Forerunner 735 (~200€) is an older model, and supports open-water swims and triathlons. You can also set up very complicated workouts (not on the watch itself though, via Android/iOS app or website).
The Forerunner 245 (~250€) or 245M(usic) (~270€) also supports configurable workouts, and the training guidance is much better, e.g. accounting for outside temperature. There’s also the option to reply from the watch (I got a reply currently playing badminton, will reply later set up), but also mobile payments and emergency notification.
Both watches support third-party apps and watchfaces. The app selection is not totally bad, but the apps tend not to be quite as polished as the built-in experience.
The 245M is attractive not only because you can play music with your watch (which some people may like to warm up), but also because you have plentiful storage, even if recording many entire training camps with extended details.
The Forerunner 645 (~280€) and 645M (~350€) add triathlon modes.
The Forerunner 945(~510€) and Fenix 6 Pro(~590€/600€/660€ depending on the size) add built-in maps to the feature set of the 645M. There are third-party apps for maps on the 645/645M, but they require a connected smartphone. I could get the third-party map apps to run from time to time, but it was very spotty, and certainly not something I’d use in a sticky situation. The Fenix 6 Pro is quite heavy for badminton though.
In general, I think the Garmin Forerunner 245 Music is the best bang for the buck: It can do even complicated training steps, and it’s a high-quality watch in general. If money is no consideration, having maps with the Forerunner 945 would be a killer feature for me. I hate that there doesn’t seem to be any competition in the market for watches with buttons and advanced features.
This shouldn’t be a problem with any of the above watches. If you just want a vibration every 7 seconds (and then maybe 3 seconds of rest), all of them can do that. More advanced stuff like showing the name of the next excercise on the watch, and varying between interval lengths is rarer.
Of the watches, the Suunto 5 can do limited HRV, and Garmin Forerunner 245 and up can do full HRV analysis. I don’t hae any data about how good that is though.
With the exception of the Corox, all of the above watches support external sensors, although the Forerunner 45 and 735 only support ANT+, and the Suunto and Polar watches only support Bluetooth Low Energy (BLE). All other mentioned Garmin watches support both ANT+ and BLE.
I didn’t really account for this, since I’m focusing somewhat on badminton. All of the above watches with the exception of the Forerunner 45 and 245/245M support openwater swimming.
Most of the watches above are about the same weight of the Ticwatch E (46g). Only the Fenix watches are heavier, with 60 to 83g.
Sports profiles default certain settings. All watches with sports profiles I have encountered allow you to change the settings at will. So if worst comes to worst, you can just use Indoor Cycling for Badminton training, and configure it to your liking. But all the watches will have Other, and many allow you to create multiple sports profiles.
By this comparison by Polar, the M does not seem to have an always-on display. [update This is wrong, see below. Vantage V is a touch watch.]
Added both to this post.
Yes, got one on my wrist right now. A nice smart watch (supports customized replies and third-party), but I can not recommend it for badminton, since it has a nasty tendency to activate the touchscreen all the time. Sure, you can lock it, but I always forget to until it’s too late and I’m in a strange submenu or screen. Plus, you have to look at the screen and touch it at specific positions for ~5 seconds to start an activity, and that sucks. On the button watches, you can usually press the start button two times and off you go. This means I often forget or avoid to start the recording.