If you change the oil you might be able to get some GL-4 manual transmission lubricant, which are supposed to work better than the GL5 multi-purpose stuff that most people (at least here in Taiwan) use, which has to be compatible with differentials..
Here's some deep-thinking (over-thinking?) on the topic.
https://www.bobistheoilguy.com/forums/ubbthreads.php/topics/1231182/synchromesh-manual-transmission-lubricants
People speak highly of the Redline manual transmisssion stuff but I've never used it.Probably pricy
I got this "Multi-Purepose" BP stuff in Japan, probably not as good as a dedicated MTL, but the best I could do.
ecx.images-amazon.com/images/I/61jxvemQTDL._SY355_...g
If there is something mechanically wrong with your gearbox though (say a failing bearing) new lube won't fix it
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