Something to keep in mind:
Avoid using mirrored consolidated lists, if possible; it deprives the original list maintainer of visits (meaning they may be less inclined to keep it up to date!) https://firebog.net/
Basically the maintained ones from: https://firebog.net/
What I want are basically containers for a browser. So I hit the button for the ‘program’ which really just launches a browser that goes to the specific address, and ideally, can retain login information, and appears as a distinct item in the task bar, with it’s own icon, and cannot simply be merged with my browser.
Sounds like you want a Progressive Web App (PWA). Really handy things, and is actually how I use Lemmy via Voyager: https://vger.app/
If you want to start small, I’d go with one supported by Asuswrt-Merlin, “a third party alternative firmware for Asus routers, with a special emphasis on tweaks and fixes rather than radical changes or collecting as many features as possible.” Keeps it close to stock with minor upgrades, and a faster release cycle for fixes. The RT-AX88U_PRO is one of the higher end routers that is supported by Merlin.