Enlarged testicles can be painful and problematic, and could very well be a *reason* why your budgie isn’t masturbating on things or overtly showing signs of sexual activity. Enlarged testes does not mean they’re filled with huge amounts of sex hormones just waiting to be released. In humans, enlarged testes is actually a diagnosed condition common with some fertility issues and can accompany low sexual drive. The testes can be fluid filled due to anatomical aberration or can swell due to viral infection, injury, they may just be over large in size, many things actually could be going on to cause the enlargement.
Testicles are a hormone producing organ, and just like any other organ, if they’re not working correctly they may not be doing the things they normally do. In this case, when you think about testes doing their job- they simply might not be. They may be damaged or irregular and not producing the normal amount of sex hormones that produce sexual urges.