There is no universal rule, in principle you could get away even with the joint test showing significant differences at 10% but not at 5%. It all depends on specifics of your research. For example, if you have large sample, coefficients will be estimated with much higher precision so using 10% level would not be reasonable (although when it comes to testing parallel trend assumption it is rare to have more than 5-10 years of pre treatment data to check for the trend).
In addition, there is no bullet proof way of testing parallel trends, you can do not just one test but battery of tests to be more confident (see literature review on various ways of testing for parallel trends in Roth 2019a or Rambachan & Roth 2020).
But generally there are no widely accepted benchmarks, some people still get away with showcasing plots that show the variables sort of move together before intervention and without rigorous testing. It varies by subfield, and is context depended, my recommendation is to either look at what other people are doing in your subfield and apply similar tests, or potentially a bit more than that if you want to go extra mile.