Is it possible to have too many priors in Bayes Theorem? Each prior restricts the sample space, so in theory, your probability becomes more and more accurate. However, if our sample space becomes too small, the tradeoff between the accurate sample and the confidence we gain from having more data points becomes apparent.
Example: Assume I want to know the odds that I will contract COVID. I ask myself what is $P(\text{getting covid} | \text{20 years old})$. Let's say I get $10\%$. Then I stack another prior to get even more accurate data. I ask myself what is $P(\text{getting covid} | \text{20 years old} \land \text{is not obese})$. Great. Even more accurate probability.
However, what if I ask myself $P(\text{getting COVID} | \text{I have a tattoo of my name on my arm})$. Let's say there are $2$ people in the world, me and my friend, who have a tattoo of my name on his/her arm. Let's say my friend got COVID. This gives me a $1$ in $2$ odds of getting COVID which dosen't make sense.
A couple of ideas - maybe Bayes Theorem should be only used as a tool, maybe the priors have to be relevant to the outcome, maybe there's a threshold below which our sample is not significant. Not sure.

There are many different ideas that you seem to be mixing and matching together.  It appears to be part of your confusion.
First, let us dispense with the idea that a prior restricts your sample space.  It does not.  It does restrict your personal beliefs about how likely it is to see any particular element of the sample space.  Suppose you believe the mean to be seven and the variance one on normally distributed data.  In that case, you should be amazed to see an observation of thirty-two.
Just because you are amazed does not imply that others would be amazed, and, certainly, Nature is unsurprised.  Bayesian probability is subjective.
The second element seems to be about the relative value of trying out different models of the world.  If your data set is large enough, the good news is that Bayesian probability is generative.  Bayesian methods favor models that are closer to the method that Nature chooses to generate data.  If the COVID virus favors tattoos, then it will impact the probabilities through the likelihood function.  As long as you compare multiple models and create probabilities that those models are the one and only valid model, you will eventually pare away the models less reflective of reality.
To work, even the unlikely cases need to have a prior distribution.
Finally, significance is not a Bayesian idea.  Bayesian probabilities are meaningful if they are meaningful to you.  It is a subjective system.  Thankfully, Bayesian probabilities do not reflect long-run frequencies.  There is a totally other set of rules if that is what you need.  Student’s t-test is a wonderful idea.
Your prior should reflect all prior knowledge about the models and parameters that you have in your possession that comes from any other source than the data itself.  You can use all kinds of other prior distributions to make other people happy, but those are not your probabilities.  If an editor wants you to use a diffuse prior distribution, you are not solving your probabilities.  You are solving his or her probabilities.  That is okay too.  Likewise, if your boss wants you to use naive Bayes, then you are solving your boss's probabilities.
However, it is true that if you are highly bigotted, then your priors will interfere with learning.  Conversely, if you are highly gullible, your prior distributions will interfere with learning if your sample is not representative of the population.  It will take much data to learn just a little bit in the former case.  It will take much data to overcome an initial unfortunate set of observations in the latter case.  It is not a trivial task to determine if your prior knowledge and beliefs reflect reality.  Of course, it is the job of the data to teach you what you thought you knew was correct or incorrect.
If your prior is too concentrated, it will slow learning if you are wrong.  If your prior is too diffuse, then it will slow learning if you get an unfortunate set of initial observations as they will concentrate around the likelihood.  Sometimes tossing ten heads in a row happens with a fair coin.  If you are naive enough, then you will believe it is a two-headed coin.  Both concentration and diffusion are problems unless they reflect your real beliefs.
