You have to do Load Calculations the official way
No, you don't get to "make up" your own method of provisioning circuits. You have to follow the official methods documented in NEC.
- The dryer is provisioned based on the data on the nameplate, which indicates its operating amps or VA. Heat pump dryers are entirely motor loads (but multiple motors) so NEC 230 applies. Hopefully the nameplate will state a minimum and maximum breaker size. I do not believe a 125% derate is applied to dryers.
- The range also has a nameplate. You must run that through NEC 220.55 to compute the size of the circuit required, however if the documentation specifies min or max breakers that too must be respected.
We can help with these calculations if you post nameplate data.
It seems extremely unlikely that both accept the same circuit breaker size.
As such you will need a subpanel to give them independent power behind their own breakers. You're not allowed to under-fuse a range or dryer, but you are allowed to oversubscribe the subpanel.
Beware 3-wire connections
Note also that "classic" 3-prong connections for ranges and dryers are dangerous as all getout, because the 3rd wire *is not ground, it is neutral. They tie the machine chassis to neutral, so when the neutral wire has a problem, it energizes the chassis of the machine and kills people - usually children who squeeze behind the dryer to fetch a ball or something, their muscles twitch madly but it doesn't push them out of contact because of the confined space. What a way to die.
If you have 4-wire supply, by all means use it.
However if you are stuck with 3-wire connections, here's a trick. Heat pump dryers don't need neutral. Ranges don't need neutral. Ovens need neutral, but only for the oven light and sometimes electronic controls. So try NOT hooking up neutral to the oven. If it still works (sans oven light) then you don't need neutral. Convert the 3rd wire to ground only and don't connect neutral.
In that case, the subpanel can be wired 3-wire with no neutral. Leave the neutral bar empty. Buy an accessory ground bar, paint it green in an obvious way, and use that for grounds. Remove the neutral bond. That way if some half-wit fits a 120V circuit later, it won't work.
Don't buy electrical gear mail order
14-50 splitter I’m considering — (link)
Well, Mr. Rockefeller, if you can afford that pricey thing you can afford to do the job properly. Clearly, cost is no object.
The problem is, that item is certainly not UL listed, and is illegal to use in this case because it will put the 10-20A heat pump dryer on a 40/50A breaker.
But the universal problem with mail order electrical (aside from being wildly overpriced when it is legitimate) is that an awful lot of what is sold is dangerous junk straight from China. It's being sold direct mail because that bypasses our product-safety apparatus (UL, FTC, all that stuff). Amazon protests that things in the Amazon Fulfillment Centers might ship to Mexico or the Virgin Islands, and FTC/CPSC has no standing to enforce Mexican codes. Then they say "well, if we shipped one to USA that was a clerical error by the 3rd party seller, who should have clicked the box to disable US sales". The lawyers have every angle figured out. The consumer safety agencies have said flat out that they don't have the annual budget for a legal fight with Amazon. But eBay, Banggood, wish.com, Aliexpress, all that is the same garbage. And overpriced too, SMH, at least you'd think dangerous junk would be cheap.
