Tethering minimum wage to median hourly wage is a good start, but might have some unintended yet foreseeable consequences, since it would incentivize employers to suppress wages to keep the median wage down, and thus lower minimum wage.

Far better would be to tether minimum wage to the cost-of-living. I explained in more detail in a different comment, but basically the formula has three variables: the monthly cost of necessities (area-dependent), the percentage of monthly income (at minimum wage) that should be expected to meet the cost of necessities (defined by legislation), and the number of hours that constitutes a month's work (also defined by legislation, for now it would be four 40-hour weeks, i.e. 160 hours).

So for example, if a state legislature chooses 50% as the proportion of monthly minimum-wage income that should be enough to meet necessities, and someone lives/works in a district where necessities cost $2000 per month, and we're using the standard workweek, the formula would look like this:

($2000 ÷ 50%) ÷ 160 = $4000 ÷ 160 = $25/hour

Which tracks with the legislation in the OP, but it's also a flexible formula which can be adapted as needed, leaves room for negotiation (e.g. states can choose what percentage to use, and whether COLA should be measured state-wide or by district) which should make it palatable to the widest audience, and it should also adjust over time as cost-of-living should be recalculated every year.