That's neat, but it requires the entire browsing session to be held on their servers, which is likely why they require you to pay for it.
There is this tool, which is similar and open source: https://github.com/ttalvitie/browservice Which can used from a computer on the network.
If we were to host it on behalf of users, it would probably need to be tied to BDNS accounts, and I'm not sure how well it would scale (or work in the first place).
But for purely using discord, you could try Discross: https://browsedns.net/topic/6438/discross-discord-on-switch-kinda

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