I think the や in this haiku should be replaced by よ (they had another や・よ mistake some days ago). But even then I don’t understand this haiku - although its general meaning is explained on the left.
What is 梅しん or 梅しんと, and what are the ‘boiled greens flavored with soy’ (ひたし - Jisho.org) doing at the end of the haiku 
?
It’s somewhat old Japanese isn’t it. I’m no expert, but maybe this gets you closer to the answer:
The 逢ひたし seems to me like old hiragana usage for 逢いたい
ひ = old kana for い + 【高校古文】「「まほし・たし」の活用と接続」 | 映像授業のTry IT (トライイット)
EDIT:
Yeah, what @Ka5 said, faster than me 
Ah, old kana would explain it. I need to study that some day, thanks!
The やう you correctly identified is also old kana spelling .
Btw, cool calendar with the explanation for the Haiku written next to it. I should get something like this as well. Each day another interesting tidbit.
Seems more interesting to me than “just” a haiku collection.
Can also recommend chapter 13 of Tobira advanced for more general information on 俳句.
や, けり, かな can sometimes be used just as a filler without any meaning as well. At first, I thought it might be that usage before understanding what is happening ^^.
Yeah, this is just leaving out the verb because it’s implied and leaves more room for his feelings of longing. The following line どうしやうもなく is actually 字余り as well, followed by the truncated あいたし which I think adds a nice emphasis.
Thank you all for your interesting contributions. I suspected some old Japanese, but then I looked up the author 駒木根淳子 and saw that she is a living person (she recently won a haiku award).
It’s no more available but I suppose there will be a 2027 edition. It is this one:
