Why is the work done by a block into a spring the same from the work done by the spring on the block?

However, in some solutions, I'm finding that "the work done on the spring is the same as the work done in the spring by the block as is an isolated system and there's no dissipation of energy". I'm confused by this.

Why is the work the same?

Work is done by forces, not by objects. The language of "work done on one object by another" is really a shorthand way to specify that we are looking at the work done by the force that one object exerts on another.

By definition, the work done by a force $mathbf F$ is, $W=intmathbf Fcdottext dmathbf x$. If we are comparing the work done on the spring by the block to the work done on the block by the spring, we are looking at $W_1=intmathbf F_{text{block}totext{spring}}cdottext dmathbf x$ and $W_2=intmathbf F_{text{spring}totext{block}}cdottext dmathbf x$ respectively. However, by Newton's third law, $mathbf F_{text{block}totext{spring}}=-mathbf F_{text{spring}totext{block}}$, and hence $W_1=-W_2$. This is true of any action-reaction pair; the work done by one force is the negative of the work done by the other force.

When your source says the work is the same, they are probably thinking in terms of absolute values. I personally don't agree with saying the work is the same, even if they are the same in magnitude, but that at least explains the imprecise terminology being used.

"the work done on the spring is the same as the work done in the spring by the block as is an isolated system and there's no dissipation of energy". I'm confused by this.

Why the work is the same?

This comes directly from the conservation of energy. $Delta U = Q - W$ where $Delta U$ is the internal energy of the system, $Q$ is the energy that comes in to the system as heat, and $W$ is the energy that leaves the system as work.

Since there is no dissipation we have $Q=0$ for both the spring and the block. Since the spring and block system is isolated we have $Delta U_{system}=Delta U_{spring}+Delta U_{block} = 0$. Then just by substitution $-W_{spring}-W_{block}=0$ so the work done by the spring on the block is equal and opposite the work done by the block on the spring.