The easy options:

As others have said, embed something existing. I think this is especially true for programming languages. Even if Lua isn't quite what you want, it's probably going to deliver a lot more value than anything you could bash together on your own. And there are a few other options as well. There are several of these "complete toolkits for DSLs", it's just they do take a bit of work to correctly insert into your code base and then expose enough of what you're doing to make it useful. There isn't and as far as I can see can't be something you just install and it magically exposes everything and it's just awesome and takes no work, because even if you're in something like Python where you can just open an interpreter shell in the current context, thereby technically giving the user the power to do anything they want, you still need to create a safe interface for them, document it, test it, etc. (You may not do a lot of technical work to keep them out of where you haven't tested but you will need to provide them a supported area to get anywhere.)

For building your own: For small tasks, a parser is just a specialized sort of deserializer. Yea verily these 30 years ago, there wasn't a lot of generic deserializers available, and the ones that existed like asn.1 were completely unsuitable for human use, so "classic" compiler literature spends a lot of time on building your own parser. Now, if you don't have a specialized need, you should use a generic deserializer. I have quite a few JSON-based syntaxes lying around. (They feed "interpreters", but same principle.) Lisp S-expressions, if suitable for your environment, can be adapted. XML could be useful in some specialized circumstances where your input looks more like a document than conventional code. Etc. You should only build a custom parser if it's going to give you more bang for your buck across the whole usage cycle than a generic parser can give you. The reason why I have several things that input JSON is precisely that the amount of usage across all time was just going to be too low to justify doing anything specialized, because it was always a strictly internal tool.

(Hint: Just because your compiler accepts JSON as input doesn't mean that that's what the humans have to directly output or edit. My biggest interpreter took in JSON but I provided abundant function helpers that abstracted that away. It was a thin enough abstraction that it could be penetrated if need be, but it avoided most of the verbosity issues as far as the humans were concerned, and gave them the full power of the programming language to generate loops and such. If you squint, I basically borrowed an existing general-purpose programming language that everyone involved already knew to use as a macro language for my language, basically for free. This means the "core" language that I was implementing didn't have to do anything that the already-existing general-purpose language could do in macros, meaning the layer the humans used offered a lot of power for not much implementation cost on my side.)

For AST transforms, this is always where your secret sauce is and there's little help to give, beyond a suggestion that this is arguably the canonical case for a functional programming style, even if you are in an otherwise OO language.

For the final output, I would suggest that in modern times, the easy answer is, don't bother. You can probably interpret fast enough to solve your problems. If not, there are some options like LLVM that will help vs. what you used to have to do. But I would definitely consider just interpreting the final AST directly. If you intend to do that your AST transforms can be built with interpretation in mind.

The real value of a compiler and what distinguishes it from any ol' normal code that ingests something and emits something is the AST in the middle, and the complexity of that AST (probably through significant recursion) and the transforms you run on it, and the corresponding complex behaviors the input can invoke through the recursive input and complex AST transforms. Anything you can do to brush away the incidental details of a compiler by using existing serializations and if at all possible simply skipping the output step of the compiler will hugely increase the bang-for-the-buck you get. You might say, rather than "writing a compiler" consider "using compiler techniques" but not writing a compiler. But not in a way the article was talking about.

For the specific case mentioned there, go get an existing parser for your language, get the full AST tree. You can write your transform in terms of what you do understand and just pass through anything you don't. It's slightly harder, but will be fairly effective.

It is possible even today, of course, that you will be backed against a wall and be forced to go through the full classical compiler cycle. A programming language, for instance, just can't afford to use any existing parser, it's too much a vital part of the experience to try to use an existing one. Even a new Lisp will probably want its own spin on S-expressions enough that it can't just pick up an existing one unchanged. And maybe you've got something that you expect will be big enough that it just requires a new syntax, and you can afford all the support that goes with that. But the vast majority of the time, with the right toolset, you can indeed obtain most of the value of compiler-like techniques without the cost of the full classical compiler technology stack, because even if it was hypothetically possible to build a "real compiler" that had its own custom syntax rather than some slightly dodgy JSON and emitted LLVM code that resulted in an executable that runs all its tasks in .0003 seconds, the engineering effort for that is so much greater than the JSON input and interpreter that runs in .003 seconds that in most cases it's not worth it.