I don't think I've ever gotten an e-mail from a band director or FA director telling me a position has been filled. They either invite me for an interview or I hear nothing aside from the application system when the job finally closes.
And just because a job posting is still up doesn't mean the job is still open. I know my current job remained posted for a while after I was hired and after I was approved by the school board and everything was official.
FWIW, you definitely should be e-mailing your resume and cover letter to both the band director and fine arts director when applying (principals can be iffy).
The following goes beyond your question, but I think it's important to understand for someone in your position.
You're in the unfortunate position of trying to find a job during a pandemic.
There are much fewer jobs available this year than have been in years past. Presumably because of uncertainty over how teaching band is going to look next year and concern over if they will even be allowed to teach band.
So you have fewer job openings but the same number of new graduates looking for jobs. It's going to be tough.
The other thing to consider is that veteran teachers who are looking to change jobs probably have a leg up on you simply due to experience. Teachers currently under contract for next school year have up until 45 days before the next school year starts to resign. After that point, the school district doesn't have to let them out of their contract. Once that deadline passes, you're more likely to see what jobs are available going to first year teachers because all the vets are locked in.
My personal story is that I did not get a job my first year. I worked as a sub for a year, including as a long term band sub. I got my first job the next summer but it wasn't until mid-July.