Also, ideally, no requirement of a smartphone to send-receive data (it's ok to need a smartphone for the initial setup of the watch, though). I know about Pebble, but it doesn't have wifi. I know about some Garmins with wifi but for the kind of apps I want to write, the communication between the watch and the server has to be mediated by a phone. Also, correct me if I'm wrong, I don't want to pay $100/year just to be able to use my custom app in apple watches. I usually don't trust Google either (e.g., they discontinue everything in a blink of an eye).
So, what are my options?
Main tradeoff: it’s very DIY (power management, UX polish, tooling). If you want less DIY, Wear OS gives a better SDK, but the platform lock-in is much stronger.
I just had to solve this problem recently. I've settled on Google Pixel Watch 4. There are some rabbit holes to go down though before it works reliably.
For me it is mainly a decoration of my drawer, but maybe comes close to what you are looking for. :)
I'm currently wearing a TicWatch Pro 3 Ultra, which has wifi, Bluetooth, and GPS. I've written personal tools for it, and its fairly painless (and free). As a developer with some background in Android, I enjoyed the experience. Getting apps approved for the app store is a pita though, as Google sets quite high bars for the review process.
I also have a Samsung Galaxy Watch4, which also has wifi. People here speak well of Pebble, which might be an option, but I have no real knowledge of it.
Finally, though, wifi is power-hungry and watches have limited batteries and endurance. Both Wear OS and WatchOS will limit wifi use by apps to conserve power, and you ultimately can't do much about that. Using Bluetooth to a phone, and its much greater wifi capacity, is a common approach.
The simplest integration is writing a daemon (in the language of your choice) that schedules wakes, syncs, and sends FreeDesktop notifications.
If you want more of a UI, then you'll be writing QtQuick, which is QML/Javascript/C++.
Their best supported watch is the TicWatch Pro: https://asteroidos.org/watches/catfish/