As shown in the linked questions, it depends.
The rules don't specify an action cost for dropping something - does this mean it has no action cost, or does it fall under "interact with an object"? If it's the first, then you can drop one focus, then "interact" to pick up the other as part of your spellcasting action. If it's the second, then you're using your "interact" to drop (or put away) your current focus, and don't have a chance to pick up the other. Ask your DM.
As an alternative, some foci might be able to be used for both sorcerer and druid. Sorcerer lists a wand; druid lists a yew wand. Sorcerer lists a staff; druid lists a wooden staff. Does this mean a single yew wand or wooden staff can be the focus for both classes? Maybe. Ask your DM.
Another alternative is a component pouch. It is a pouch you can hang on your belt, that contains all material components that don't have listed costs. This can be used by all spellcasting classes, no question. And drawing out the components is covered by "interact", so can be done as part of the spellcasting action.