This is a pretty hard topic to concisely summarize.
In general, one way to answer your question is
The hardness of LWE is precisely what the Lattice Estimator says it is.
This is reductive, and almost certainly not true. Still, it is perhaps the most useful thing to say.
Roughly speaking, if we define $T_{\mathsf{LWE}}(n,m,q,\sigma)$ as the time to break LWE with
- dimension $n$,
- number of samples $m$
- ciphertext modulus $q$, and
- gaussian paramter $\sigma$,
then $T_{\mathsf{LWE}}(n,m,q,\sigma)$ doesn't have any particularly nice closed-form expression.
Other problems $P$ in cryptography often have one "best known attack" for general parameters, and you can summarize $T_P$ in terms of this best-known attack.
For example
- RSA has the general number field sieve
- Discrete log has index calculus (in the finite field setting) or any $O(\sqrt{|G|})$ generic group algorithm (such as Pohlig-Hellman),
- Code-based crypto has intersection-set decoding type algorithms (I believe I say "Prange's Algorithm" here, but I'm not a code-based person).
LWE has at least three relevant attacks, namely
- the primal attack,
- the dual attack, and
- Arora-Ge.
This is to say that $T_{\mathsf{LWE}} = \min(T_{\mathsf{Primal}}, T_{\mathsf{Dual}}, T_{\mathsf{Arora-Ge}})$, and therefore doesn't have the nicest closed-form solution.
This (and that LWE has so many non-trivial parameters, i.e. 4 compared to 1 for things like RSA) is (roughly) why people use things like the lattice estimator instead.
You might find this prior answer to be useful (in particular, links to some dissertations on algorithms for solving LWE in various parameter ranges).
In short, I'll point out that your assumption that errors are contained within $\{-1,0,1\}$ is very strong, and opens you up to attacks like Arora Ge (though you need $O(n^3)$ LWE samples, which is on the high end in certain applications).
The general answer I would give though is to just use the lattice estimator, and perhaps read the dissertations linked in the other answer if you want more background on the general theory behind it.
