I assume you know of all the usual suspects for getting old Macintosh software. If not, here's a list.
https://vintagemacmuseum.com/resources/mac-software/
That being said, what you want to do is really not possible. The only "somewhat" modern web browser for Mac OS 8.6-9 is Classilla, and it's far from perfect. It's basically 20 year old Mozilla code with backported features from more modern versions of Firefox. It's not stable, it's very slow, it has lots of bugs and most important of all, it doesn't support all modern web standards.
The only two solutions I can offer you are -
First, you can create a local web proxy server somewhere on the LAN that your Macintosh can see and have a HTTPS stripper on it. Modern web encryption is very slow on old PowerPC CPUs, and Classilla doesn't properly support all of the various types of encryption used. One problem it won't fix is Javascript and HTML5, which modern websites make extensive use of. These two items can cause Classilla to freeze or crash the whole machine since classic Mac OS was cooperatively multitasked.
Second, spin up a simple HTTP server on the LAN you can easily dump files on and use this to get files on your old Macintosh. I'd recommend this method over the first, because it'll be the fastest on older machines. If you want a fancy page to display your files, you can use an older CMS that is light on resources, like Autoindex
https://sourceforge.net/projects/autoindex/