I always prefer simplicity, full control and flexibility.

1. Basic analysis, system design and architecture, determination of what packages/tools/frameworks/whatever to use and install,
2. New project in IDE, new local host, new dev server, new DB, installation of some other tools/languages/packages/plugins/drivers in rare case and basic, usually default, configuration (if you are lead, you, usually, also need to make some access for team members),
3. Installing all the main packages/frameworks via composer require and npm install, whatever you use,
4. After that there might be some private packages/modules added, usually via same package managers or a bit of copy paste from previous projects and templates.
5. Writing main architecture, usually couple of empty services/objects/classes/functions, which are filled a bit later, so here main point is to design core API and how core components will be communicating with each other
6. In case of backend usually it's Laravel, Lumen or Vanilla PHP,
7. Basic core DB structure and migrations,
8. In case of frontend I use Vanilla JS with some simple libraries including BunnyJS and Bunny Assets Builder which provides me components and bundling/transpiling out of the box without any configuration. I don't use any CSS frameworks like Bootstrap anymore, has own CSSNext basic set of helpers and grid. Here I also have everything ready for building SVG sprites.
9. There also should be some linters like ESLint, CSSLint, PHP sniffer tools, whatever (Usually such stuff should be already installed and configured on IDE level)
10. If you still don't have git repository, then git init and adding it to your server or just GitLab/GitHub,
11. If you are building a package, then npm init, composer init, whatever,
12. Talking about the developer-designer cooperation and extracting assets this is never done at the beginning and is not related to scaffolding, while designers might have own templates and libraries, set of icons/images/color pallets/whatever; developers will see some assets and design much later and it's not developer's job to extract assets. Instructions and assets should be provided by any professional designer.
13. (Optional), some docs, wiki, CI, deploy scripts,
14. (Optional) New project/board in Trello/JIRA/whatever, team management, granting access. In case of JIRA as an admin you would waste days configuring this bs :/
15. (Optional) New emails, groups, file sharing setting up or at least google drive and anything else you (or your team) need(s) to start working on a project seriously.

In simple words, at the end I and my team should have version control available on the server for everyone, all the main architecture, folders, packages, build tools installed and configured. Usually it doesn't takes me a lot of time. What you mean by scaffolding takes me couple of minutes while "scaffolding" basic design and core architecture of the system takes a bit longer.

This process is really flexible and is unique per project.

I just have a simple skeleton app with the required folder structure, some files with basic scaffold code, and a suitable package.json which I just copy over for any new project.