PBS will continue to pay $$$, possibly more $$$ for US Rights, but I would suspect that those rights would be only for Premiere and then only for a short time. PBS is still a great source of income to BBC. However, PBS is not the only source of programming for local public television stations. Some of the most popular shows on local stations is Brit programming from 3rd party APT or other sources, which includes content from BBC, Channel 4, and other TV commercial services in the UK. However, while almost all of that content is also available at Hulu and/or Netflix, less so Amazon, I've noticed that neither streaming service has the latest series until AFTER the lcoal stations have premiered that content and can't as long as a YEAR. Of course, content that does not fit local public TV stations image will be part of that "premiered 24 hours later" stuff on the new service to be launched.
In other words, I doubt much will change for PBS and 3rd party providers because they are a cash cow now to the Brits, and PBS would be DEAD without Brit content and would pay whatever it might take, especially content from BBC, as those prime-time shows fuel the fundraisers for the local stations, who in turn pay ridiculous amounts in dues to PBS for rights to the PBS National Program Service. PBS and locals also funded by CPB for all sorts of other costs.
Also, concurrent rights for a number of different channels or platforms is often the case and can be the case here, while reserving exclusive premieres for the new service when necessary, but then exclusive only for a fairly short time.