As someone else pointed out, some companies still offer vacation time and sick leave separately. None of the companies I've worked for still do, all have combined those into a single Paid Time Off pool.
An allotted amount of "sick days" doesn't really make sense anyway, not like you can choose to be sick next year.
(Only exception is for long term sicknesses, if you are sick for more than 6 consecutive weeks, then the next week your health insurance will pay you 60% of your normal wage instead. Or if there is no hope of you ever being able to work, again insurance.)
Oh and if you are sick on vacation you get your vacation days back as you were not really able to take advantage of them.
I really disagree strongly with trying to push things onto companies.
The government want to pay basic income? Great! The government want to provide health care? Great!
This to me is the main advantage I like about basic income, is it really seems like we can get rid of all these suboptimal laws with horrible abuses and bad tradeoffs, including: - min wage - overtime - vacation requirements - healthcare requirements
So businesses can just focus on what they do best and the government provides a safety net.
In Germany it's just more structured. There's multiple special rules, like the employee must be working at the company for a while, it has different rules for companies with fewer employees, companies can't be in an emergency situation, there might be the possibility tax rebates.
This is mostly handled by careful accounting. You need to provision future money for it rather than living in a reverse "paycheck to paycheck" situation. I never had a German company but I had a company in a country with similar arrangements and my accountant made me learn it all.
It also has the side effect of having businesses to care about employee quality of life. Someone working 12 hours a day will probably burn out quickly.
More or less everyone has a 5-day week. Most jobs offer 25-30 days/year + unlimited sick days