Interesting that Czech has "dear" meaning expensive just like in English.
Not completely sure, but I think "drahý" is only used with the meaning of expensive/costly. My former employer in the Czech Republic used to call me "milý" + my first name ("dear...").
No, it is also used in the meaning of "dear" as in "Dear customer,...". But II
(Next try. Writing this from my smartphone.) No, it is also used in the meaning of "dear" as in "Dear customer,...". In my monolingual Czech dictionary one of its meaning is "milý, milovaný". But I think you are right, insofar as it seems to be very rarely used in colloquial Czech. Probably you'll be more likely to find it in a formal or written context. Perhaps a native Czech speaker couldnexplain the details to us.
It is old-fadhioned, but possible. More likely in a hand-written love-letter than in an e-mail.
You can also call your SO just drahý/drahá. Quite formal/old-fashioned. You can see it in old movies or in fairy-tales used among the upper classes.
But a colloquial form is drahoušek (masculine for people of all genders). That is widespread. And you can call a group of people "drahoušci, drahouškové". That is very colloquial.