I’ve got a Thinkpad 600X (Pentium III, 256MB RAM). I put Debian 12 on it, and the OS is not quite small enough. (NetBSD couldn’t drive my particular CardBus Wifi card, sadly, and 9front couldn’t drive the NeoMagic video properly.) Just Emacs on the console, no X, and eww for web browsing (to your question) and elpher for poking around Gemini. I’m not familiar enough with Thinkpads to know if that’s a useful data point for you.
Nobody’s mentioned https://www.haiku-os.org/ yet, so I will. I can’t remember what happened with it on my Thinkpad. There are several graphical browsers there, with a range of capabilities, as well as a port of Emacs.
I guess my real answer is: don’t handle today’s internet with all of its heavy websites? Use the web for documents, and use native applications rather than web apps for other purposes, such as chatting and email.
No, I have not tried that. But I might now. :)