It's definitely less than 90 seconds but I haven't timed it...probably somewhere in the realm of 20-30 seconds.
I'd be very surprised if it was the watch losing internet and, aside from your comment about the wake timeout being 90 seconds, the rest of the evidence so far doesn't really point in that direction — for one thing, this happens everywhere, regardless of watch connection method. When I'm at home and the watch is directly connected to strong Wifi, and out and about when it's using the phone's cellular connection. It's pretty reliable that it will fail no matter what/where I am these days. Second, I have no other watch apps showing any such symptoms of spotty connection. Additionally, if the car is already awake — like I just parked it, or I woke it up by opening the Tesla app or by opening a door — the Tessie watch app works fine with no hiccups. It connects within a couple seconds of opening and displays current state. There's no timeouts/loss of connection issues, etc. It's only when waking is initiated by the Tessie watch app that it now frequently fails, whereas it used to work fine 90%+ of the time.
I feel like this started right after one of the Tesla updates in the last month or so, but I can't be sure when I first noticed it and whether it really correlates to the car software updates. Currently the car is on 2023.44.30.8.
If there's any other data I can collect or anything I should try to narrow down the issue, please let me know.