The Apple Watch Series 4, Series 5 and Series 6 come in case sizes of 40 mm and 44 mm, so they're the same. As long as you get the same size for the new Apple Watch, the existing straps you have will fit well with no problem. While I think the new straps will be labeled 41 mm and 45 mm, that doesn't mean they won't work with older watches. Currently, all straps have 40 mm or 44 mm labels, but are specified to work with older models in most cases.
Unfortunately, Apple Watch straps aren't universal. Since the older Series 3 straps fit all Series 6 and SE, Apple Watch fans have a lot of straps. You can install the new Apple Watch Series 6 if you use the same size (38 mm for the old Apple Watch straps and 40 mm for the new ones) as the old ones. There are several Apple Watch straps that don't fit all wrists and others that are designed to fit some but not others.
It's not necessary to have a different size case for the Apple Watch Series 5; simply select the strap that matches your model on the Apple website. That means that a strap on a Series 3 watch could be noticeably too small for the Series 7, since a difference of 3 mm between 42 mm and 45 mm could be a bridge too far away. Until Apple makes a big design change with the Apple Watch, any strap you have that works with a square shape will work. The Apple Watch Series 7 will be announced soon, almost certainly on Tuesday, September 14 (here's why).
Weinbach's information that the new Apple Watch “will use different straps that won't be compatible with old watches” is open to interpretation, at best. While the Apple Watch has been around for many years, Apple has maintained the same tab design every year. It's not clear if the reason bands like Milanese Loop aren't available is because Apple simply doesn't want to ship more 40mm or 44mm straps on them or because the Milanese Loop will need a redesign to match the flat-edged case. The Apple Fitness app, available for free on the App Store, can help you achieve your daily training goals.
However, if you have a strap for a 42mm or 44mm cover and you want to use it on a 38mm cover, the strap won't stretch and won't fit. Since the link bracelet has a diameter of 135 mm, it is slightly larger than other Apple Watch straps. So that means that Apple has to make new straps that are compatible with older versions at least with the SE or make straps that only work for this year's models, once again unlikely to the point of being unthinkable. The Apple Watch straps sold to date are compatible with all Apple Watch cases that measure 38 mm or 42 mm.