It is possible to create a web browser in assembler. There have been several attempts, some of which have been more or less successful.
MenuetOS 64bit has a browser inside, like an author written in assembler. Unfortunately, the project is closed, so it cannot be verified.
KolibriOS has a lightweight browser (although a rather limited feature).
The main problem of such projects is that there are not enough people on them. As a rule, assembly programmers have different interests, and these days they are too small to spend time programming a web browser.
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