Remove the stray space at the end.

This "or " is not localizable (i.e. just concatenating it into a diagnostic means that it might not translate correctly in another language.

I think that this is a little too general. You really only want to recommend "set" when the element access is on the left hand side of some mutating operator (e.g. =, +=, ++, etc.). You want to try to recommend "get" otherwise.

I would try to avoid (and remove) these comments regarding error messages in general. The baselines should communicate that on their own.

The arg count is incorrect for set methods (it should probably be 2).

Unfortunately symbolToString might not work if the expression isn't a simple binding. You'd be better off with something like

const suggestedMethod = isAssignmentTarget(expr) ? "set" : "get";
if (!hasProp(suggestedMethod)) {
    return undefined;
}

let suggestion = tryGetPropertyAccessOrIdentifierToString(expr);
if (suggestion === undefined) {
    suggestion = suggestedMethod;
}
else {
    suggestion += "." + suggestedMethod;
}

where you could define tryGetPropertyAccessOrIdentifierToString in utilities.ts.

function tryGetPropertyAccessOrIdentifierToString(expr: Expression): string | undefined {
    if (isPropertyAccessExpression(expr)) {
        return tryGetPropertyAccessOrIdentifierToString(expr.expression) + "." + x.name;
    }
    if (isIdentifier(expr)) {
        return unescapeLeadingUnderscores(expr.escapedText);
    }
    return undefined;
}

Right! Let me do this in a few. Thank you.

Other nit - use suggestion !== undefined.