When "who" is the object of the preposition, as in this case, it becomes "whom"; granted, this is by now vestigial and often ignored in informal conversation. You'll often hear people say things like, "Who should I give this to?" It would be correct to say "Whom should I give this to?" and misguided fussbudgets will insist you render it as "To whom should I give this?" But almost no one bothers with that these days. Note that reversing the word order makes the incorrect grammar stand out: "I should give this to who?" That's because there is now a direct apposition with the preposition and its object. Most careful speakers will use "to whom" in that context.
You can remember when to use "who/whom" by substituting "he/him" in the sentence. You wouldn't say "I'm doing the project with he," you would say "I'm doing the project with him." So it's obvious that whom is the pronoun you would use here, not who.
A further word about German/English prepositions. In German some prepositions can be dative or accusative, depending on whether they indicate motion or placement towards or up to a location. This not the case (no pun intended) in English. In English, the object of the preposition always takes the "prepositional" case. Note that there are not nearly as many inflectional changes or pronoun substitutions in English as in German. The point is, German is not necessarily useful for analogizing English constructions.
One relevant piece of data (although I wouldn't say it's conclusive) is the case of the singular second person pronoun thou/thee in archaic English, since this pronoun had distinct forms for the subjective and objective cases and was used in the vocative fairly often.
When it was used in the vocative, the nominative form thou seems to have been used, as demonstrated by this quote from Shakespeare:
Kent. Thou whoreson zed! thou unnecessary letter! (King Lear, 2.2.35)
Similarly, back when ye was still used as the subject case form of you, the sources I have found indicate it was also used for the vocative (The English Language; Its Grammar, History and Literature, by John Miller Dow Meiklejohn), although as ye passed out of use the situation seems to have become less consistent (An English Grammar, by Eduard Adolf Maetzner, mentions some grammarians who describe ye being used in the nominative and you in the vocative).
I think it's fairly unnatural to use a non-second-person pronoun in the vocative, so I don't have any strong intuitions on "dear he" vs. "dear him" and I'd guess that different people would have different preferences here. Guifa has left some comments suggesting "Dear me" sounds better than "Dear I"; I guess I'd agree, but I can't think of a situation where I'd use either and both of these options sound awkward to me (I think people normally use second-person pronouns to talk to themselves, as in "You've got to keep going!")
I'd recommend going with the nominative "Dear [whoever]."
Another piece of data may be that in present-day German, which has retained case to a greater degree than English, the adjective corresponding to "Dear" is put in the nominative singular form when addressing a letter: one writes "Lieber [name of a male]" at the start of a letter in German rather than using dative "Liebem" or accusative "Lieben".
Not all languages with cases deal with such situations the same way: in Ancient Greek, it seems that the receiver of the letter might be given in the dative case at the start of the letter (according to Alexandre Daubricourt's answer to the following Latin SE question: Are there any surviving Ancient Greek letters (epistolary)?).
English is more closely related to German than it is to Greek, but even closely related languages can sometimes use cases differently, so the German data is not conclusive with regard to English—it only suggests that the nominative case is a plausible candidate in this kind of context.
Best Answer
I'm not really sure what you mean by "dative" in English, as there isn't really an accusative/dative distinction - in situations where other languages might use a dative, either the accusative is used ("I gave him the book") or a preposition ("I gave the book to him"). However, the following might be helpful in articulating why "who" can be used, and may even sound better, where some insist on "whom" - whereas in other situations "whom" is still preferable:
To make my explanation clearer (at the expense of much precision, for which please forgive me) I'll refer to two "styles" of English - one very formal (in which the who/whom/whom prescribed by the style guides is compulsory), and one much more colloquial (in which who/who/who rules the roost, and "whom" is seldom if ever used). Very loosely speaking these correspond to English as it was both spoken and written in the past, and how it is most often spoken today; since trends in the written form often follow those in the spoken we might see current written English as being in a transition between the two.
Given all that, the sentence:
entirely follows the rules of the formal style, and is thus acceptable.
entirely follows the rules of the more colloquial style, and is thus acceptable
However, the sentence
grates. This seems to be because it follows neither the rules of the formal style (which would have "to whom"), nor the colloquial style (which would instead have "The man I gave the ball to yesterday was tall", or a variant thereof), and is thus unacceptable in either. Similarly,
also falls between both stools.
Note that this is largely handwaving, rather than a rigorous argument, but it's interesting to note that studies have been performed in cultures exhibiting diglossia (i.e. using "high" and "low" variant forms of what by some definitions could be considered one language, in different contexts) where subjects were shown words or sentences combining features of the "low" and "high" variants. It was found that some of the features were only weakly associated with one variant or another, in the sense that (say) using one from the low variant in a sentence otherwise fully "high" would not render it unacceptable; however other features were "strong" in the sense that a sentence containing features strongly associated with "high" and others with "low" would definitely render the sentence unacceptable. It is possible that, on a much smaller scale, a similar phenomenon is going on here (though of course it would be very bold to assert that this is the case without much more rigorous research!)