We will try to understand the cases through cases described in Gemara, to examin the similarities and the dissimilarities. The OP says:
They were left in such a way that they seemed to be Hefker.
I even overheard a few people saying "I guess these are the leftover Esrogim and the guy selling them left them for anyone to take".
In Baba Metsia the Mishna said:
מצא פירות מפוזרין מעות מפוזרות... הרי אלו שלו
If he found scattered fruits (on the ground) they belong to him.
א''ר עוקבא בר חמא במכנשתא דבי דרי עסקינן קב בארבע אמות דנפיש טרחייהו לא טרח איניש ולא הדר אתי ושקיל להו אפקורי מפקר להו
There are fruits abandoned on the spot. The owners is not going to bother to pick them up. Gemara discussed for the value, quantity, size and concentration of fruits. The purpose is to evaluate if the effort is worthwhile. If it is the case, the owner will come back.
We have a goods, it can be grain (generally when the mishna says "perot", this is wheat), of any kind of good. The circumstances suggest that a small amount of the goods was abandoned.
Here in our case the owners were aware that some esrogs leftover there. But despite this, they have not bothered to come back to take them. The place is not a secure place. Thus, the owner left them intentionally and this is called "Aveda midaat" (an intentional loss) as one who junk a seal in a non secure place. They innocently testimonied that esrogs were intentionally abandoned. They cannot come after the Holiday and expect payment. Maximum they can take the esrogs if they are still here. But even this is no more their property. Why a synagogue is not a secure place? This is a public place and non-Jewish persons often are cleaning up the spill. Children can damage the Esrogim. and to leave even not intentionally a valuable object in such a place maybe automatically considered as yeush. Gemara told about bate knesiot and makom she akum metsuyim.
Thus we have strong reasons to validate the mitsva without paying.
See SA CM 260, 7. and 261, 4