The error/warning is coming from your linter, not VS Code. Also, Convert to template string is a refactoring not a quick fix, so it's not expected to show up in the quick fix menu.

I've update the issue title so this issue only tracks enabling convert to template string in cases where the first part of an expression is not a string literal

Self contained example:

const obj = { prop: '123' };
const z = obj.prop + 'b' + 'c'

1. Select obj.prop and try triggering code actions

Not that familiar with the code, but sounds like this would be a matter of checking for other node kinds, (e.g. Identifier, PropertyAccess, ElementAccess, ParenthesizedExpressions), skipping those nodes until you reach something else, and checking if that node is a + expression

Perhaps worth clarifying (as the subject changed and is not 100% accurate from my observations), the refactoring to template literal will work if the first part of the expression is anything other than a dotted object.property reference. In addition to string literals, simple variables, and numeric literals all work -- not just bare "strings".

const x = 'y';
const w = x + 'A' + 'B';
const z = 5 + 'a' + 'b';

It is only obj.prop at the beginning that will cause it to just shrug and make you do it manually.

Thanks @mjbvz for pointing out that it is tslint raising the refactoring suggestion. I understand tslint is being deprecated for eslint, but I've had no luck converting a large project over to eslint despite following the migration guide. I'm unable to test if eslint has this same issue. If not, perhaps the fix lies there.

And if tslint v1.2.3 is still being maintained by Microsoft, it would be nice if clicking the Quick Fix ... (Ctrl+.) link in the popup dialog worked as advertised -- that is, the behavior you get only if using the keyboard Ctrl+. option or the Show Fixes (Ctrl+.) menu.

Is this a good issue to get into the TypeScript codebase? Unwound line to contribute to TypeScript during Hacktoberfest and if it makes sense would start with this issue :)