I'm thinking October 15th is too soon.
Just three weeks between iPhone 13 launch and an Apple Watch Series 7 launch seems too short for there not to be a date set from the first announcement.
Why?
Well:
For them not to put a date on it usually means there is uncertainty on their end around manufacturing, yields, etc., as opposed to them just being coy. This is especially the case here since the watch is on such a regular update cycle now. This delay is definitely the result of something going wrong.
The first gen iPad Pro, iPhone X, and iPhone 12 mini and Pro Max had 'long' (in Apple terms) periods between announcement and launch - but had a fixed launch date (or at least month) from the get go.
Other products with no fixed date had a long time until they arrived, e.g. original AirPods. Not three weeks.
Finally, when Apple gives a seasonal time window, they normally hit the end of that window, e.g. original Apple Watch ('early 2015'; shipped May), 2013 Mac Pro ('late 2013'; shipped December), 2019 Mac Pro ('late 2019'; shipped December).
Will happily eat my words though.