Sorry, no. There are a lot of people who would like that! Here’s the Apple support guide on adding complications. I think the best you can do at the moment is at a watch face with eight complications, the Infograph, which is what I have now.
I was going to write a description of how to do this but I thought a video might be easier to follow. To get the point I started at open the Shortcuts app and then Automation tab at the bottom of the screen. This is where the video starts.
Edit: Just watching the video back I’ve realised it has not clear that after clicking the plus sign in the top right of the screen the next thing to choose id ‘Create Personal Automation’. The screen recording on my phone has not captured the screen presses but hopefully you will be able to work out the rest of the screen presses. Please let me know if anything is not that clear.
This is one of the easier automated Shortcuts to set up:
In the Shortcuts app, tap the Automation button at the bottom (the clock). Tap the plus button to add a new “personal” automation. Select “time of day” and set the time you want to run the automation. After you tap Next, you can add the Action to “Set Watch Face”.
I think it’s easiest to search for the action (rather than scroll through all of the options). But you can also get to it by selecting Apps under the search bar and scrolling down to Watch. Once you’ve added the action to the shortcut, you can select which watch face to switch to by tapping on the word (variable) “Face” in the action itself.
I set this up on my phone that controls the Apple watch. I’m not sure if all of these options would appear on, say, an iPad, that’s connected to the same Apple ID.
I use HomeRun on my watch to control specific scenes. I think I have the original version, however, version 2 is listed in the App Store. From what I can see this allows you to control your selected scenes from your iPhone and iPad, as well as on the watch face.
There’s a free trial and then you can pay a monthly/yearly subscription, or a one of payment.