Might not be what you had in mind, but NixOS “kind-of” ticks all your boxes.
For me NixOS is a build your own distro more so than Arch could ever be.
My config covers antiquated meme worthy notebooks with 4gb ram, desktop with an ultra wide monitor and dedicated graphics, two headless servers running services, containers, transcoding video / cctv; aaand my daily driver laptop.
As far as 2nd hand laptop are concerned - it’s very location specific. My neck of the woods it’s buy online or hope some locally has marked something at a reasonable price.
Picked up a laptop with a busted screen $30 cheaper than the RPI 5. 1135G7, 8gb upgradable ram, m.2 storage, wifi, bluetooth and a battery.
Raspberry pis’ were great early on, but their appeal has quickly diminished in my eyes considering used hardware options that are available now.
Size would be the one redeeming quality of a raspberry pi for me, my headless laptop is thin but takes up substantially more space.
Creating a browser from scratch is a monumental task, ladybird is such a project which has been in progress since ~2022, and will probably take another couple before it’s at beta. Optimistic release is 2028, or ~6 years of development.
I’ve moved to schizofox (NixOS) but there are plenty of other forks available which remove telemetry and other default behaviours from Firefox.
Chromium forks are another alternative however due to chromiums dominance in the browser space I’m reluctant to shoutout any forks.