How do I predict new/unknown data in Bayesian linear regression?
Let me help you get started -


you don't get a single value here like you get in linear regression,rather posterior distribution of the parameters. yes, The output here is generated from a normal (Gaussian) Distribution characterized by a mean and variance , nothing special I am afraid. But depending on the mean and variance you can determine which price is more likely to be.
yes its not a real valued number like price here but the probability ,output is the likelihood multiplied by the prior probability of the data.


Here is a very simple explanation, I couldn't put it in better words-

https://towardsdatascience.com/introduction-to-bayesian-linear-regression-e66e60791ea7

And here is the more mathematical background with this chapter from stanford-

http://cs229.stanford.edu/section/cs229-gaussian_processes.pdf

and you are not alone as these Author's agree-

"Gaussian process regression models, though perhaps somewhat tricky to understand
conceptually, nonetheless lead to simple and straightforward linear algebra implementations"