I'm not a lawyer
but
The GPL does not require publishing your source to the public. This requires that you distribute the source along with the application if you distribute (sell, etc.) the application to someone.
LGPL doesn't even require this; it requires that you distribute the sources of the library (and any changes you make to it); not the application itself.
If users access your web browser through a browser, this is not considered distribution of the application. (there is an AGPL for this)
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