Any site design will look stale after five years, no matter what standards you follow. It's just an unfortunate reality, there is no way off of the wheel unless you are like Craigslist and deliberately reject all convention.
This? https://www.mcmaster.com/
On desktop, sure. But they don't work in mobile. And that's easily 80% of the troubles of modern design: to avoid building everything twice, today people write "responsive", "mobile first" websites that, on desktop, tend to have an excessive amount of whitespace and other issues (see for example the old vs new reddit layout)
What's being demanded of websites in 2023 is just much more difficult to do well than what people wanted in 2010.
Also many of the interactions with governmental digital services happen only once a year. I've been in helpdesk supporting people on a webapp with an obnoxious interface that they had to use 3 to 4 times a year to fulfill their project report in order to get paid for their project work. The UX was so out of the conventions that people hated it with passion and I had to help the laggards to use the application.
In extreme cases of very large products whose owners want them to look exceedingly modern it can be like painting the Golden Gate Bridge: by the time they finish implementing the last components and icons, the ones that were implemented at the beginning of the project are already due for an update.
The job security simply isn't worth the maddening repetition.
/you may get the impression I'm bitter.
(btw your solution is needlessly complicated and way too much hard work - easier to sit with the client, exhale deeply then say "A full redesign? Thats quite a big project and its a lot of work, are you sure?" offer a fixed rate contract assuming 100's or even 1000's of person-hours and deliver (after a polite overrun of a few weeks) the updated css.)
/you may get the impression I'm bitter and cynical.
it's not my solution, it's the solution I'm suffering through because our styling, as determined by external company, is handled via Chakra UI meaning that redesign requires JS work.