TL;DR: This is going to be tricky because of your age and perceived lack of life experience. Her anxiety is her problem, and she's forcing you to pretend so she will feel less anxious. As an adult, that's not appropriate. I apologize for knowing nothing about Hinduism, so be forewarned I may be wrong about a lot of what I say.
However, in situations of distress, its like a switch flips on in her head that puts her in religious overdrive. That means... she starts enforcing her beliefs onto me. (emphasis mine)
I don't know how much 'analysis' you've done about your mother's problem. I know you've expressed yours:
I feel like I'm living for others and I can never assert myself to my parents without them always finding a way to convince me I'm wrong...
Your mom, when anxious, retreats into her religious beliefs because, for her, it is a way to exert some control over seemingly uncontrollable situations. That's very common, and there are many non-religious counterparts, e.g. any superstition (stepping onto a plane with one's left foot first will prevent the plane from crashing.) So it's not necessary to address her or your religious beliefs with her; what's more important is that you need to help her see that her anxieties - where you're not the cause - are hers to handle, not yours.
You'll encounter some problems with this, first because in the eyes of your parents, you're still a child and you should be obedient/respectful, and second, because the idea that one should take care of one's own anxieties oneself is foreign to many people.
To really do this (if you must), first be prepared. Read about anxiety, the causes, and the proven methods used to cope with it (for example, meditating and journaling.) Second, anticipate her counterarguments and don't go down rabbit holes about religion, respect, etc. Third, practice your spiel, because it will require all your restraint to avoid having the conversation devolve into an argument over opinions (like if you should believe as she does.)
Approach this all very, very respectfully. Request a time to have a serious conversation, tell her it's about something that's been troubling you lately, let her pick the time, make sure you're both relatively relaxed and the time is quiet and of adequate duration.
Then tell your mom what you've been reading about (anxiety) and how some people handle it (turning to God/gods, meditation, journaling.) Tell her in the most respectful way possible that you've noticed she turns to religion in times of anxiety/distress. Let her know that you respect this. Let her know that you love her, and you care about how she feels. Make sure you repeat that last sentence a few times, and that she hears it. Then comes the 'confession' (which she already knows, so it needs only mentioning once: that as you don't share her religious beliefs. Then politely tell her that you believe her asking you to observe certain rituals to take care of her anxiety is like asking you to journal to take away her anxiety.
You meditating for her anxiety to get better won't work.
You journaling for her anxiety to get better won't work.
You acting religious for her anxiety is not appropriate, because it's a demand to do something that is a pretense for you, for her anxiety.
This is a fact. It's not a feeling, it's not an issue of respect, it's not about obedience. It's just a fact.
Repeat the sentence she needs to hear, that you love her and care how she feels, but, since you're not a believer, you would rather do something to help her lessen her anxiety, like listen to her talk about it, or taking a walk with her someplace nice where she can feel some peace, or something like that - something that will help her to manage her anxiety (keep repeating those words politely.
I don't know how she will react, but don't argue about anything: accusations, her distress that you're not religious, why you should be religious, etc. Just deal with what is: you do not believe. This is her anxiety. She needs to find a way to deal with it effectively (with your help if need be) herself, because someday soon, you will be out of the house and she will still have to deal with it.
I believe this discussion will need to occur several times before it sinks in. But this is what setting a boundary is all about. To be honest, it's unusual for a youth of 16 to set a boundary with their parent that is this subtle. They might have no problem with you staying out later with friends or asking for privacy (also a boundary). But this is more delicate, not because of religion, but because you're in essence asking an adult - your mom - to act like an adult.
You can also read about setting boundaries with parents and how difficult that can be.
If you try this, I hope it works for you.