For how long will the 19.07 (old stable) branch continue to receive support? Or in general how is the support for an old stable handled?
There is no such info on the homepage afaict, maybe somewhere else? In any case I think it would be a nice bit of information to add somewhere on the website - even just in form of estimation - to decide and plan an eventual migration.
There is no official word yet, but the plan has always been to drop 19.07.x as soon as possible (after the release of 21.02.0) and to divert the focus on 21.02.x and the next major release beyond that.
While there may be a final wrap-up release for 19.07.x in the future, I wouldn't plan with openwrt-19.07 into the future and rather schedule the migration to 21.02.x soon.