Re-organize Bash scripts

### What would you like to be added?

This is a follow-up on https://github.com/etcd-io/etcd/pull/20850#discussion_r2459235292.

Currently, our Bash scripts follow a custom convention of defining the `Makefile` targets as "passes" that are in the `scripts/{test,build,etc}.sh` files. This custom (and undocumented) way of maintaining the scripts is difficult to follow by new contributors. Because of this, we currently don't have a standard and have a lot of duplication in our `Makefile`, spread across different files, and approaches to run these targets/functionality.

### Examples of fragmented architecture

1. Custom "PASSES" framework: https://github.com/etcd-io/etcd/blob/855c9ba31e1a1ab58eb30368baeb873760325cef/Makefile#L109-L111
2. Executing a Bash script: https://github.com/etcd-io/etcd/blob/855c9ba31e1a1ab58eb30368baeb873760325cef/Makefile#L229-L231
3. Embedded scripts in the `Makefile` target: https://github.com/etcd-io/etcd/blob/855c9ba31e1a1ab58eb30368baeb873760325cef/Makefile#L171-L178

We want to simplify and standardize this, without creating a difficult custom framework to implement and maintain.

### Why is this needed?

To improve the maintainability of our Bash scripts.