@lpetiti So if we summarize here: the client didn't send you the materials within the deadlines outlined in the contract, they did not message you to let you know they'd be late or let you know when they would send you the manuscript, and when you reached out to them they said they'd message you back and then didn't. But YOU are worrying about being thought of as unprofessional
Let me just reassure you here: they are the ones being unprofessional, not you. Trying to get your materials so you can do your work within the deadlines isn't unprofessional. Reaching out to them when they fail to contact you isn't unprofessional.
What is professional? Getting the project done. Making sure you get what you need to get the project done. Maintaining communication with them.
I doubt you emailed the author saying "Hey Btch, where's my fcking manuscript??!?!?!" So you really have nothing to worry about. Polite, calm, clear and honest communication IS professional.
If I were in your shoes, I would have emailed them ages ago, being polite but candid. Asking them if something is wrong, if there's a problem with the project (maybe due to Covid) and letting them know we're going to have to re-draw a new contract with adjusted deadlines. Let them know you understand this is a difficult time and anything can happen, and you wish to maintain communication. That understanding what's going on with the project and when/if it can be expected to resume is important because you need this information to organize your schedule. You can reiterate you love working with her, you love the project, and no matter what's going on you wish to work with her to find a solution and get this wonderful book done.
As long as you are being nice and polite, you should never be afraid that communicating with your client is going to make you look unprofessional. I think you've been exceedingly patient and understanding considering the circumstances. This client has been very unprofessional and should be counting their lucky stars that you still wish to work with her after all this.