There's a difference between individual businesses and overall inflation.
First, a lot of jobs pay over the minimum wage already. Raising minimum wag will not raise the salaries of those workers, and therefore will not change production costs.
Second, some businesses are less labor intensive. That is, labor is a less significant factor in the operating costs of the business. For example, retail. Most of the cost at checkout is the wholesale cost of the item, which is likely not affected by minimum wage. (I'm unaware of many US manufacturing jobs that pay at or near minimum.) So increasing retail clerk wages, while it will increase operating costs for the store, it will probably not do so significantly.
But a service, where the main component of operating expenses is labor
will have operating costs that are significantly tied to the labor cost. I interpret a care giving service to have mostly labor expenses. Yes, there are supplies, advertising, insurance, and office space for administration. But mostly labor. In such a business, a 30% increase in wages is going to increase operating expenses significantly. Maybe not quite 30%, but maybe 20%. (It depends on what the other expenses are.) that has to be paid either by charging a higher rate or reducing profits margin. (If it's a government agency, it would require increasing the agency's budget.)
If this is a private firm, there's the possibility that they will reduce their profits
somewhat, but I doubt they would absorb the whole thing.
For support:
https://www.1800homecare.com/blog/medicare-openly-penalizes-home-health-agencies-that-dont-game-the-system/
So if the profit margin is around 9%, an increase of operating costs of 20% eliminates the profit entirely and puts you into the red. If it's a small agency, like the one that cared for my mom until recently, the owner's income would be entirely wiped out. So I think they would have to pass the cost along in their rates or cease to do business.
But the impact on one business sector or even the low wage sector may not be enough to affect overall inflation rates noticeably.