So far, looking into some kind of combined browser and email client application
that may still find some usefulness or support in pre-OS X systems is limited...
Just a browser: Classilla for MacOS 9
http://www.floodgap.com/software/classilla/
Download Classilla 9.3.3 from SourceForge (23.7MB, StuffIt archive)
http://www.floodgap.com/software/classilla/releases/
There had been some kind of Thunderbird version for PPC but unlikely
that custom build (like TenFourFox, but by a different group) would run
in old classic MacOS9.2.2. The following is an example of PPC build
for Tiger 10.4 & Leopard 10.5, a custom build using Mozilla code...
Tenfourbird. Tenfourbird is a mail user agent for PowerPC based Mac OS X.
Tenfourbird based on Mozilla Thunderbird and TenFourFox. Latest version is 38.9.0.
tenfourbird.osdn.jp
iCab, a german browser, may have an email client aspect. iCab305_PPC_E.sit
Haven't updated this for a few years and if using as browser, GMail doesn't
see it as capable of connecting with their latest 'improvements'. I have one of
the last versions for G3/G4 that runs in Tiger/Leopard in PPC. The last version
iCab for Classic MacOS 8.5 - 9.2.2 is available from 'blue link iCab305' above.
FAQs suggest little for Classic here: http://www.icab.de/faq.html
As to web browser(s) - one by name 'Classilla' based on mozilla/wamcom code
seems to be available. Not sure how Gmail Login (instead of Client application)
would work. Unsupported browsers are an issue with more recent macOS X.
There are some older SeaMonkey versions that pre-date the arrival of OS X.
They are unsupported and likely won't access much online; they did have an
email client section such as successful 'multi-purpose' apps back in the day.
Most of these have been for the last supported builds under OS X. And they
are not being supported now.
If your iBook G3 2001 model (white) has a Combo optical drive, it may be able
to see & use Tiger OS X 10.4 retail DVD installer media. Otherwise much harder
do get (and costly) 4-CD installer kits were limited in number & scarce by now.
For the present retail cost of a 4CD Tiger 10.4 installer kit, you can buy a good
working MacBook 13-inch early model; these can run Snow Leopard 10.6.8.
Anyway, this has taken a little time as I've been reading into bookmarked sites
to see where that path had taken obsolete and vintage Mac users. Little to see.
Good luck in this matter!