How do people make custom Pokemon for Pokemon Sword & Shield?

Based on some of the fields that they are saying can be set in this transaction, they are using a 3rd party program to generate the new pokemon.

For instance, trainer name/trainer ID cannot be set easily (and trainer ID is random). For them to be able to set these to whatever you choose, it would take an unreasonable amount of time restarting a game to get the correct combination.

Also, to ensure the perfect combination of nature, IVs (set at time of catch, not to be confused with EVs), etc. of a shiny pokemon of any variety of your choosing would take an immense amount of time and luck.

As is seen on your second posting, the seller usually have some sort of "disclaimer" saying they will provide any legal pokemon (no impossible movesets, no lvl 1 legendary, etc.), presumably to avoid detection of anti-cheating measures during & after trade.

They are using the older unpatched Switch with PKHeX in order to edit pokemon.

It is legitimate in the sense that you can use it in online ranked battles as the pokemon themselves are legal and practically impossible to tell that it has been hacked if done correctly.

Also, in addition to what the parameters you have mentioned, it is also possible to edit how you met the pokemon, on what date, pokeball captured in and ribbons, which further boosts the legitimacy.