It is very unusual for a device to go missing from the Find My app, unless somebody made a mistake! Check which watch is really connected.
On the new watch, (short) press the Digital Crown to reveal all the apps, go to
Settings (grey cog wheel) / Tap your name (the top entry in the list) then check your Apple ID sign-in
Look in Apps again, look for a green icon with outline computer screen and iPhone (Find Devices) and scroll down the list, check what you can see connected and findable.
I suggest taking a look at Apple's comments in these support documents (written for different purpose but it might help you check).
About Activation Lock on your Apple Watch - Apple Support
What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support
Worst case, if you really can't find your Series 9 anywhere in Find My, you might have to unpair and re-pair to setup again.